when should I start my Oxbridge personal statement?

You should be starting now if you plan to apply this year and say that you will defer the year as the deadline for oxbridge is the middle of October. Or you can apply next year to start 2023. Normally people start their personal statements in the summer before they apply. Hope that makes sense.

I started writing mine at the start of September and will be applying in a month

I didn't think it was very difficult as I already knew what I wanted to write about. I just got it read by our university adviser/coordinator and then redrafted it based on his recommendations. I also got it checked by my subject teachers for them to look over the content I included, and my GCSE English teacher to make sure it was well written.
I'm applying for Maths

If you're not applying for another year it may not be too worth writing a full statement yet, as you will likely gain other things you want to write about in a years time.

It never hurts to start writing down notes and ideas though. Fairly early on i just had a document online and for months i would write down any ideas i had, examples i could think of and things i did as they came to me. This made it easier to write the statement in the end, as all my ideas and examples were there and just needing organising and writing up.

I would say try to aim to get the statement finsihed at least a week or two before you intend to send it though, a day or two after completion is always when i get those 'i should have added this' moments

I'm actually planning to apply next year for 2023 since I'm taking a gap year, so should I start my ps next summer?

No we know that you're planning on applying for 2023, but you could still apply in this cycle for deferred entry (so starting in 2023). If you wanted to maximise your chances of getting in you could apply this year for deferred entry and if you don't get in, apply AGAIN next year, but you might have left it a bit late to do that

well the deadline is in 3 weeks and i did absolutely zero preparation

You could look at it like you've got three weeks to prepare. It's possible to write a good personal statement in that time and might be worth a shot. You have nothing to lose as at worst you just apply again next year but you may have some extra experience with the interview or something.

but I have mocks next week and I did no reading or any Oxbridge prep

Like i say, you've got nothing to lose and everything to gain. Even if you can only spend a week on it .

I'm in year 13 but I'm applying for 2023 since I'm taking a gap year due to medical complications, I already started the prep though as in I read some recommended books

U can still apply this year but put deferred entry on ur UCAS form or u could apply after u've left. It's a good idea to start about now as the deadline is soon

well I guess I'll apply for deferred entry 2023 and If i don't get in, I can always apply next year and I need to take a gap year since it's not a choice but crucial for my treatment, so I really did no prep but I can possibly read a book or two and watch stuff ig and then immediately work on my PS

I don't think u'll be able to apply for 2023 entry next year if u apply for deferred entry this year. If u don't get in u'll have to apply for deferred entry next year and not start till 2024