The characters don't feel finished in-game due to act 3 so why are people burnt out when it's not finished?
Burn out doesn't require completion of task to occur.
The game was in development for 6 years, then after release they spent even more time working on it with the patches.
Working on the same game for 6+ years can become tiring, especially if you as a team keep having to overcome hurdles due to working around the D&D ruleset which is more restrictive than your own IP's you've previously worked on.
Did act 1 take up most of their time so they ran out of time in act 3?
Pretty much.
Act 1 was developed along with Early Access. Meaning 3+ years out of the total 6 was spent on Act 1.
Then they remembered there's 2 more Acts in the game...
It's a recurring theme for Larian's development. Work excessively on Act 1 with help of Early Access feedback... Then remember the rest of the game exists and crank out whatever they can in the remaining development time.
Honestly, it's probably a factor in their burn out too. When you hyper fixate on Act 1, spending lots of time and resources meticulously crafting it... Then you look at Act 2 and Act 3 and think "Aww hell naw, I'm not doing all that work 2 more times..."