Timeline is as follows and perhaps you can also advise when when its likely that we will get PPR based on this timeline
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Pre-arrival services letter 19 May
The pre-arrival services is the most relevant part that you should have mentioned. (Most applicants get the medical request at the early stage of application). Even so, you are overthinking and you should probably renew ASAP jsut as everyone has said so far.
No-one can tell you though how long PPR might take - in general, but as also not clear what country (Pakistan?).
I still would suggest getting passport renewed but now with a tiny bit more nuance: if you are CERTAIN that you would depart as soon as you got the COPR and you KNOW that passport renewal takes eg four months or more, perhaps - but still probably no. If you are in Pakistan, renew the passport and forget all the above, because you don't know when flight bans will be lifted anyway, so there is no sense.
And note: passport request letter often says (ours did anyway) to 'ensure that your passport is valid for at least 12 months from the date of this letter.' (I do not know how strict they are about this).
I am much more confident that IRCC would let you submit passports with some delay if you demonstrated that you had applied for new passports because their validity was too short.
Anyway, up to you, but if any issues, it's your problem, not mine.