Is there a realistic way a person having an old computer and cheap (but not free) electricity can actually mine monero equal to some amount which can be used to donate to good service providers or purchase services?
I keep hearing about low reward to effort ration, but can I get a respectable amount in let’s say a year without having to deanonymize myself by going to a Centralised exchange?


Sure, but nobody is checking that, and if you were such high profile that you thought somebody would be, you just stop a few stranger and ask for change for a 20 etc and the numbers tracking will dissolve quickly.
If you /OP are that paranoid about cash, crypto is worse, its a full ledger of every transaction.
And mining it is not anonymity because the proof you mined it has to be checked in the entire system.