Open mailing lists often have public archives, for example https://www.mail-archive.com/. Many lists are subscribed to multiple public archives.

Those archives are often searchable on their own platforms, and are indexed by regular search engines too.

Now about mailing lists created using the google "groups" platform itself, is a different story. Does google index it's own group archives? No idea. Those were _already_ horrible to look at before and I've subscribed most of the ones I follow to other public archives to get something usable.

Traditionally if you're subscribed to a mailing list you'd basically have your own local archive of it and use your email client for search. If you wanted to incorporate messages from before you joined the list, you'd ask some old-timer to send you their mbox archive.

Public/centralized archives as the sibling notes became common at some point, though usability is generally worse than with an email client (at least the power-user ones).