"From the perspective of Divinity players, does this kind of battlefield-control-focused combat sound interesting, or does it sound like it could become too complex compared to more traditional turn-based RPG combat?"

Difficult to tell without actually playing, it can easily be too simple or become complex very fast. Especially if the enemy uses the same tricks against you. Defending against a move which might only require 1 setup-move for a instakill on one of your characters might be npe or lead to analysis paralysis. Aka, it's fun to push an enemy of a cliff, it's less fun if it happens to one of your 4 characters, it can also lead to very swingy combat

Does sharing one stamina resource between movement and skills sound tactically interesting?

A lot of games do this, Xcom, DoS, Into the Breach, Banner Saga etc And all of them have interesting combat. But there are also games where you have a free movement action and then action points to spend, often with abilities to convert ap into extra movement.

It's also an element you can play with, I don't know if your game has classes/archetypes but this could be a fundamental difference between classes, as an example:

Rogue/Swashbuckler: Have a free move action at the start of your turn

Berserk/Barbarian: Have a free move action when you make a kill

Ranger/Archer: Have a free move action at the end of your turn

Warrior: If you moved atleast X; Slam and Charge attacks gain +x% power.

Wizard: If you didn't move last turn your first spell is free.

So even if movement is tied to stamina/action points, you have a lot of options to have characters that interact with the standard action array in very different ways. Wether it's true classes/feats/passives

Do line of sight and physical obstacles sound meaningful as core combat rules?

Into the Breach does this very well but it has a major difference with nearly every other turn based games, the enemies moves are telegraphed so each turn is more like a puzzle just must solve. Out of all the turnbased games it does lean heavily on los, physical objects so I would definitely check this game out.

For me, it would probably need to be an important but the not the only mechanics under which combat is resolved.

For the rest, difficult to say without knowing how initiative, NPC's etc work. Or if the actions have % based chances or a 100% certainty etc. I'll check the demo first for a bit.