This sounds really hard for you, no wonder you're exhausted.
I think you need to set different standards and expectations around her play, talk about them with her and stick to them.
Before my ex moved out, he became quite ill and I went through a similar change myself, where I'd have to be responsible for doing bedtime etc alone with 3 small DCs and realised that I couldn't just count on cleaning up later (or someone else doing it).
Things that help:
It takes a few weeks to set this, but she needs to learn how to tidy up before starting something new. You can turn the tidying up into an activity, or if it's a big mess we pile it all into a heap and set a song via Alexa (my older ones like the 'tidy up rumba' as they use it at school, but can be anything high energy!) and see if you can dance while you do it and put things properly away by the end of the song. If you can get the older ones involved (with bribery if necessary
this will become much easier)
Max of 2 items out at once (e.g. Barbies and a puzzle, if she then wants to get out Lego, one of the others has to go away). Again, this takes some time, but when they know it's non-negotiable, they will do it
No dinner until the living area is clear (I do sometimes find weird things shoved under the sofa, but at least it looks nicer!)
Getting her involved with as many practical activities as possible. She's old enough to help with cooking, or sorting sock pairs in the laundry or dusting skirting boards, it will again take a bit longer but you'll save time and misery on tidying and she may enjoy it too
Sounds like you do lots of activities but does she get lots of exercise? I find that helps a bit.
Do you have high door handles / stair gates / other ways of keeping her within one zone? It's definitely harder once they want to roam!
Worst case, strategically timed TV. I had to do this with my very active dc2, with the others I'd use TV to have an occasional coffee break but with her it was my time to do stuff fast, which was a bit depressing but as you say, isn't forever
Can the older children help too? Even if they do some Duplo or dolls with her while you do something urgent, it will help and is good for their bond too.
Last one, might be a mindset thing... When you say she's 34 months, I wonder if in your head she's still a baby and not 'nearly 3', which most people would say? I have the same temptation with my youngest sometimes, and find it helps to think in year not monthly terms and to have realistic but high expectations, it will help you all.
I'm sure plenty of this you're doing, but hopefully something helps!