Apparently, “porcelain chip fix” epoxy survives about a year in a bathroom sink:
It came loose from the drain rim while I was cleaning the sink; I wasn’t doing anything particularly vigorous.
The stain in the lower right goes all the way around the epoxy:
For what should be obvious reasons, I was loathe to scuff up the sink surface to give the epoxy a better grip, so it couldn’t make a watertight seal all the way around.
A closer look at the stain:
I’m reasonably sure that’s iron bacteria colony, rather than actual rust, as there’s no iron to be found anywhere nearby.
For lack of anything smarter, I’ll apply another dose of the same epoxy, although this time I won’t be expecting a long-term fix.