All the data you submit to these services is stored on servers I run. Currently, that refers to a VPS I rent from DigitalOcean. I may also find an object storage provider in the future for media uploads, and I'll list that here if/when I do.
Any information you submit to federated services may also be stored by other servers on the network out of my control, for example a public post on Sharkey will go to the servers of your followers, or a Matrix message will go to the recipient's homeserver.
I will never share any of your data with third parties (with the above exceptions) or use it for advertising.
While I won't go snooping myself, direct messages on Fediverse services are not end-to-end encrypted and I cannot make them end-to-end encrypted. You should use a different service for sensitive communications. I have Matrix for that, though if you really value security you shouldn't depend on me. Use Signal or something.
My SearXNG instance keeps no logs.