Is it better to euthanize a cat when they reach old age?

‌My cat is 13 now, so it's not time yet, but
their activity level has definitely decreased, and seeing them occasionally make litter box mistakes
makes me realize they are indeed getting old.
When they are in a lot of pain due to old age,
some people choose to prolong life through surgery, while others choose euthanasia.
I haven't thought deeply about which side I should choose yet, but...
it seems like a very difficult decision.
Also, I am raising two cat brothers,
and I've heard rumors that if one passes away, the other follows shortly after. Is that true?