Because Accrescent isn't accepting applications currently, the next best option is Obtanium. This is a FOSS Android app which can be used to automatically check for updates of apps you install directly from the source. I have not yet been able to make it work with Nextcloud as a source, but it can scrape an index page that points to the APKs or pull directly from GitHub Releases, among other sources.
Obtanium has another benefit in that it's set up to work directly with AppVerifier, which handles verifying the authenticity of the application and ensures it has not been tampered with since the APK was signed. Hashes of the signing certificate(s) will need to be shared. For AppVerifier to compare against, which people can copy to their clipboard and paste into AppVerifier.
Suggestion TL;DR:
- Add Obtanium support by providing an index of releases with direct links or publishing to GitHub Releases.
- Publish signing certificate hashes for use with AppVerifier.