How well will side-questing be handled?

Well, Bioware did say they took inspiration from Witcher 3's sidequests this time around instead of DA:I. And we haven't really seen anything much about sidecontent other than the loyalty missions. My guess is that it's going to be a mix of both fully-fledged sidequests and fetchquests. We do have a crafting system which means we will be scanning for resources throughout the game. It will be inevitable that some quests make use of that scanning system.

My only hope is that they minimize the fetchquests as much as possible. That was my number one issue with DA:I. The overwhelming amount of fetchquests was what turned me away from making more playthroughs on that game (Which is crazy, as I usually makes dozens of playthroughs on Bioware games).

The reason you're thinking this way is because MEA has the journal on the screen updating your quest progression as you go, unlike the first trilogy.

In Thane's recruitment mission when you get to the elevator you're not told you need to clear out the henchmen in the room, but you assume so because A. it's a linear level without any other options to advance, and B. because the closed elevator infront of you is blocked by a number of mercs.

In an open world where you have so many directions to go to, especially if you have a mission inside said open worlds you need these simple guidelines of "Find X" "Collect Y for X" and "Kill a number of Zs in order to advance towards X".

Even the lauded Witcher 3 did this.

I'm confident. I am confident because of the way they are handling the marketing. Back when we got the Crestwood demo in DA I it was clear that it was just an example of what a quest might mean. It was a conglomaration of your typical DA I quest all told and was not supposed to be indicitive of either side quests or main quests. Fast forward to the Game Awards video and the quest we saw was a lot more likely a side quest. A nice little murder mystery side quest to boot which seemed to involve an actual story, IE meeting with Kelly and then going out in the outback to investigate. This quest by itself already looks about better then 80% of the side quests we got in DA I.

Besides BioWare has done good side quests before, they just need to remember how to do them.

It's not Mass Effect unless the sidequests are stupid in some way.

ME1: Oh, race against time? Let's poke around random planets forever.
ME2: No dialogue from your friends, minimal dialogue from Shepard, and that whole messy race against time thing again.
ME3: Sidequest by eavesdropping!

Toooo be fair to Mass Effect 3, there were a lot of sidequests (Mass Effect 2 companions, Citadel ones, the ones Hackett gives you) that were pretty much everything you WANT in a sidequest...

But it doesn't exactly reduce the awkwardness factor of "Hey, I managed to find the thing you were talking about kthxbai."

Great.
Now I officially can't sleep.

If ME:A is like this ... no. Especially with that grin. Otherwise maybe.

Perhaps BioWare should drop companions and instead devote its stories and writing to side quests. Perhaps then people will be satisfied.

Well Geralt spends like half of the last three books bitching that he should do that alone, so wish granted.   I would have loved a few semi permanent companions à la Milva, Regis, Cahir and Angoulême, but in the end is good that CDPR went that way, I already have BioWare for companions, and I like variety in my games.

Edit: That should read half of all the books, but I feel generous today.

Back on topic, I'm confident they got the feedback from Inquisition. They have repeated several times they don't want filler quests, and that they got inspiration from Witcher 3, where sidequests were the best from the game. Now how exactly they implemented these ideas is anyone's guess at this point.

The thing about side missions for me it's that is preferable quality over quantity. Personally, I don't need nowhere near 60-80 hours of side-quests and I would rather have half of those (maybe even a third) and have some more resources devoted to each of them. I don't know if this could left the big maps a little empty, but I don't really need that many big maps either...

In any case, I'm optimistic about MEA

See, I agree that the main 'zone quests' as you call them were really well done and interesting. And there were some great little 'stories within stories' if you looked around those areas as you moved through the quest in letters and journals and such. I don't think Inquisition gets enough credit for those. Even some of those side quests you got in the war table were pretty cool. It's unfortunate that the complete lack of cutscenes and face-to-face conversations took so much away from them though. I think that was a huge mistake on the developer's part, which I hope MEA learns from. Otherwise, the quality of the storytelling wasn't bad at all. But if they do take inspiration from The Witcher 3, which supposedly has very good sidequests, then, cool. I have no issues with them learning from games that do certain things well. And I did think Inquisition did a lot well. The fetch quests weren't one of them, because they felt more like an overwhelming chore list than a fun set of optionals:

Shard collection, else I miss out on exploring one of the most beautiful cavern in the game and some character buffs and a neat bit of lore.
Astrariums, which offered the best equipment, a neat puzzle, and more lore.
Mosaic pieces, which, again, if you're lore nerd are hard to ignore, and it gets you more dialogue from sorta interesting dwarf guy.
Elven artifacts for Solas, circle books for Vivienne, warden stuff for Blackwall, so on and so forth if I want a bit of extra companion dialogue or an extra quest....
Bottles - which, okay, I can ignore those, but I don't necessarily know that's what I'm searching for.
Fetch quests for starving villagers and stuff - okay I can ignore those I suppose.
Bring note A to tree B - I suppose I can force myself to not care about that.
Requisitions - I did learn not to bother with those unless I happened to have the stuff.
I want to specialize! - Wait, another fetch quest....? 
I want to customize Skyhold! - Resource gathering, you don't say.... 
I want to craft/upgrade my potions! - Right, resource gathering it is.... 

It was just waaaayyyyyy too much! I know all of those are optional, and are supposed to encourage you to explore, and I do like to explore. The problem with the exploration in DAI is that the areas were so large, and so densely packed with repetitive enemy encounters, I didn't feel like exploring was very fun. I'm that lore nerd who loves to read every codec and explore every stupid cave and talk to every person and find every note.... but on the way I had to fight 15 identical groups of Venatori, and another 10 identical pack of wolves, and if I picked up that journal page, I'd have to backtrack and find the other five, which meant a whole lot of walking around in circles in search mode. And then I'd turn in that ram meat or that letter to a grieving lover and I'd get rewarded with a distant conversation with a character whose face I barely saw, or an excess of power points I had nothing to spend on. So they didn't even feel rewarding to me as a player. Even the war table missions - there were some very cool ones, but outside of reading stuff, it didn't seem to matter 90% of the time what you chose to do. There was no dialogue outside the war room with anyone, I didn't get to meet the majority of the characters I was reading about, and so on.

Now, I actually loved Inquisition. While I didn't find the main plot particularly strong or the main villain particularly compelling, I did enjoy the main quests a lot. As  you said, the main side quest for each area was typically well done too. The companions and side characters and party banter were the best we've ever seen. The romances were varied and felt a lot more natural than before. The amount of lore we got was fantastic, the crafting I actually found fun for the first time, and the environments were beautiful. Unfortunately the side quests, for all their potential, fell flat in some way or another, or just lacked that something that made me feel like, yes, I feel accomplished. I feel satisfied with what I just did. I feel rewarded. That was worth it.

Anyway, there's my criticism of Inquisition, in a very large nutshell. And why I think it's fine if they take inspiration from it as long as they improve on it instead of going 'that was good enough.' Because in the end it unfortunately wasn't. I think that's where that quality over quantity thing comes in. I would have preferred they removed a handful of those things I mentioned if it meant they could've allocated the resources to elevating others.

They also counted as exploration, at least according to Chris Priestley

Witchers majority of the time do work alone