A server's Local timeline shows all the public posts by people on that server in chronological order. (On the official Mastodon app, Local is called "Community".)

If you want to browse the Local timeline of another server, go to its website and click on "Local". You don't need to be logged in.

If you want to follow another server's Local timeline within a Mastodon app, try the third party apps Fedilab or Subway Tooter on Android, or Ice Cubes on iPhone/iPad.

More info: https://fedi.tips/how-do-i-browse-the-local-timelines-of-other-servers-on-mastodon-can-i-follow-other-servers-local-timelines-from-my-account