You can use Mastodon through an alternative web client if you prefer. One of the most popular is Pinafore, which is lightweight and FOSS.
The example website is at https://pinafore.social
The source code is at https://github.com/nolanlawson/pinafore
Because it's free and open source, you can host the web client yourself if you want to.
Its creator has written an introductory post with more info about it:
A small self-hosted server for myself and my friends.