Chrome apparently has (and had for over a decade) a custom Priority=High attribute for cookies to help determine which ones should be evicted when the number of cookies hits the quota. Maybe we should make use of it.

(I don't think we had any issues with Chrome evicting session cookies before, but we had it with Firefox and it was quite painful to debug and mitigate: T151770: Frequent loss of session data in Firefox (since around 2016-11-28))