Misskey turns their off by default (you can easily turn it on within settings) & Mastodon requires you to implement the #ElasticSearch code on your instance. I use search on both of my solo instances.
Misskey does not have an official app, but #MissRirica replicates most (if not all) of the options on the web interface (something most official apps on other platforms can not do yet).
You can ask the admin of the Mastodon instance to install it as it is very useful. I wish it was enabled by default but I think it is intentionally left out.
"Big wiki projects have text in a lot of different languages—which use several dozen writing systems—as well as technical symbols, uncommon character variants, and all kinds of “interesting” formatting and typography. As much as possible, we want that kind of thing to be transparent to searchers."
this enables full-text search for posts you haven't interacted with, as well as full-text search for accounts, and includes several advanced filtering operators and parser fixes.