Sorry you're obviously correct about sieve. Maybe I misremember about server side search in mutt (not sure if there is a difference to neomutt), but I remember imap search was very slow if caching was not enabled (IIRC there's even a warning in the mutt documentation about this).
And I could be wrong, but AFAIK neomutt at least supports server side search.
1. https://www.ietf.org/rfc/rfc9051.html#name-search-command 2. https://tools.ietf.org/html/rfc5228