In general, you do have to manually download and install updates. However, some apps will automatically check and download their own updates. Also, if the APK is available on a site such as Github or Gitlab, there is an app called Obtainium that you can use. It will notify you when an update is available, and download and install it for you if you choose: https://github.com/ImranR98/Obtainium
As a trans person, I feel far safer on Lemmy and mastodon than I ever did on any other social media.