You have the right problem, but the wrong solution.
It's hard but what you need to communicate back is that I have X no. of things on my plate, and please help prioritise what is more urgent. And then doing A, B, C first means expect D, C afterwards. Under promise and over deliver.
I know we have that innate feeling to be the 'pristine Superman self who can do it all' image to our colleagues. But no we are humans and there's limits to what's humanely doable.
This is negotiating on the core problem - think from managers pov, if you negotiate on work priority and timelines, they only have a small worry and small action item to do than say when hearing 'you are looking out' and very likely they will also do something impulsive (it's just human thing).
This will be a negotition with pushback from both sides:
- Most like scenario they will agree with your delivery timelines and give inputs on prioritise coz they don't know how much load is on your plate.
- in a medium resistance case, where you to and fro propose expectations and you make it clear that you understand and pushback - this will be remembered by manager going forward with all task assignment.
- Worst case - the extremely overloaded with work case like you mentioned going through will only happens very rarely since you created a negotiation barrier meaning manager has to justify it really well - like a big product release with tight deadlines, or any special case (not for business as usual stuff).
So to summarise - talk to your manager and discuss on the expectations. Very likely this should help with work load. In the off chance they push back fully and not even give any room to decrease and show some toxic traits suggesting you will be fired and all - then you still stand your ground. Show you are not happy or aligned. That will signal to them in good context that you will be leaving. (This is so much better than you telling you will be leaving without give reason or chance for manager to fix).