I'm sorry you're so stressed.
sounds like you could do with being with someone more willing to pull their weight & shoulder more responsibility, but I'm also guessing now isn't a good time to be thinking about splitting up with your partner, so maybe you need to 'work with what you've got'.
will he do stuff if you ask him?
is he reliable if you hand over responsibility for xyz to him?
at the very least us he ANY use if you say something like 'this weekend we need to pack up the garage, shed, spare room & tidy up the garden, so please don't make any other plans. I'll make an order for boxes & tape etc can you please collect it early Saturday morning? Then ask him to start on the shed.
or, obviously, whatever things suit you.
pack up as much as you can, as soon as you can. Number the boxes and keep a list of roughly what's in each & which room they're from. whenever/wherever you move to this will need to be done, so no point waiting.
There's no point saying 'don't worry' (like asking the tide to stop coming in), but try to remember that it is just moving house, it will happen at some time.