The traditional way as a mailing list subscriber is to automatically filter incoming messages of each mailing list into a dedicated folder, which builds you an archive from when you first joined. In addition, mailing list servers (at least used to) provide zip archives of messages by month/year in mbox format that you can import into your local folder. When that wasn’t available, I sometimes asked long-time subscribers for a copy of their archive. The benefit is that you are not dependent on whatever search tooling the list server provides, but can use the email client of your choice, and you still have the archive in case the list server shuts down.