I understand your position about DnD, and I already mentioned that it will be hard for Larian to walk middle ground in BG3.
Regarding actions - no, characters do not 'need' lot of actions, but it certainly helps. You need large number of combinations per fight in order to really have "tactical options" and chances for synergies. And combinations are influenced by number of choices AND number of actions per fight.
In chess, you have only one 'action per turn', but you have large number of choices per each turn ( 16 figures where some can move to 8-16 different spots, some to only 2, but lets say around 80 choices ). So in 4 turn 'fight' in chess you could theoretically select your 'tactics' out of 80^4= 40 million combinations. If we only look at 'meaningful' choices, ie those that make sense, then its much less, but still on each move you could probably on average consider dozens of potentially valid moves. Which means that 4-turn fight in chess still has 20k combinations - plenty to ensure that you need to *think* and tactically select best option, as opposed to just play whatever is available.
If we look at BG3, you have one main action per turn and one bonus action. Melee/ranged classes have only few main actions, and all have also just several bonus actions. So you have around dozen potential combinations of choices per turn, but that is total number - you have much less 'meaningful' choices, and you often end up in BG3 using same actions each turn, or selecting among 3-4 different turn plays at most. That means 4-turn fight in BG has just 256 meaningful combinations, not even comparable to chess.
Now, as I said, TWO things increase number of possible combinations: number of choices ( spells, attacks, cantrips, bonus actions...), and number of actions. But out of those two, number of actions has MORE influence.
Consider hypothetical game where you have 3 meaningful choices per action and 2 actions per turn ( BG3 is close to that ) - In 4 turn fight you would have total of 3^8= 6500 combinations. Now, if we double number of potential choices (spells, bonuses...) we increase that to 6^8= 1.6M in theory, but in practice not all added spells will be meaningful or often used, so its much more modest increase. On the other hand, if we double number of actions per turn, keeping same spells and choices, we now have 3^16= 43M combinations - about 40x more than if we doubled number of available spells/bonuses . And, while most of these numbers are just guesstimate ballparks to illustrate my point, incidentally those 40M combinations with 4 actions per turn is comparable to 40M combinations in chess 4 turns.
But since gamers do not play game by enumerating all combinations, above is just to illustrate that 'more actions per turn' is more potent way to increase tactical variability.
So I do believe that BOTH more actions per turn, AND more choices per action ( spells, attacks, bonuses ) all increase number of tactical options and make combat more interesting.
But apart from cold math, there is also my experience from games that allow 4-5 actions per turn: it is MUCH easier in those to use interesting but not very powerful spells, thus it is MUCH more natural to get synergies in such game. In DoS2, you have lets say 8 AP per turn. Your normal attacks are usually 2 AP, your stronger attacks/spells are 3AP, and smaller/helper/bonus spells ate 1AP. It is obvious that you have much more tactical opinions from start at each turn - do I use 2 big or 3 normal attacks? If I use 2 big, it may still be less damage than 3 normal, but can I add some 1ap helper spell like haste or clarity or ... ? So you end up not only using 2-3 attacks per turn, you also often have choice to use some smaller spell that you would RARELY use in BG3 if it means you must forgo your only attack.
In short, single main action per turn means you simply can NOT use smaller, more interesting but weaker spells/attacks, if you want to play optimally. While in DoS2 and similar games with multiple actions per turn you CAN, without intentionally playing worse than if you used just attacks.
I'm sure this discussion has been done elsewhere on these forums, as it is part of "like DoS" vs "true DnD", so I just wanted to explain why I think more actions are good.
But again, I understand position of DnD players, and I agree that BG3 *was* advertised as DnD game. It may be that I personally find DnD rules as negative thing or inferior to DoS rules, but I'm sure there are many DnD players who think otherwise. Also, even if I consider BG3 worse than DoS2, I still consider BG3 as good game - and even if Larian makes it more DnD I will still plays it ( well, except if they remove advantage on higher ground - that would be showstopper for me I guess ). But I also believe there are many more casual non-DnD players that may be lost to BG3 if it become more DnD.
In regards of tactical depth, the number of actions is not very important, in my opinion. The game needs to be balanced around the number of actions every participant has, but apart from that, it doesn't really matter.
If every participant has 10 actions per round, then of course you have to make sure that you have enough meaningful things to do in that round, and that you still get a certain amount of rounds. If every fight is over after only 1 round, it would get boring fast. The same, if every fight takes 100 rounds, then probably every fight will feel like a chore after some time.
As you said yourself, it needs to feel like you are doing something meaningful every round.
And I think you can achieve that with DnD quite well. There are ~495 spells, and approximately 75 feats. Every class has also distinct abilities and flavours. And e.g. for the spells, there are not many redundancies. E.g. Bless is the only spell, that adds to your to-hit chance per se. Of course there are other spells that give advantage, which also results in a better to hit chance, but mechanically different.
What's different now in DnD compared to DOS is that I can't use powerful abilities very often - the more powerful, the less often I can use it. In DOS after 3 rounds or so you can reuse every ability. In DnD I can use a spell like 4 times ... Then my characters have to rest. So I need way way more planing and tactical thinking when to use which spell or ability. Because resting is not always possible, especially if I am in a dungeon.
If I now use 1 - 2 (DnD) or 2 - 3 abilities/spells per character per turn (do I use 1 small ability and 1 big ability, or 3 small abilities in DOS) does not make much difference when you are controlling 5 or 6 characters, at least in my opinion.
I am the same opinion as you, it's the synergies that count, and there are lots of them in DnD.
Sadly right now we don't have a lot of spells and feats implemented in bg3. And those that are in the game are not always implemented correctly. Same goes for mechanics.
So I understand completely that you think the combat in BG3 is lacking. It absolutely is.
But it really depends on Larian to implement the core stuff for level 1 - 4. Then - I am quite sure of it - there would be quite more choices per turn. And you would also get other possibilities to get advantage than just from height, namely through tactical usage of your spells and abilities.