Obtainium

Obtainium allows you to install and update apps directly from their release pages, and receive notifications when new releases are made available.

Each source can be configured with various filters and settings to account for different release schemes, edge cases, and user preferences.

For everything else, a generic "HTML" source can be customized to find and extract APK info.

It also provides a way to import/export data and share app configurations with other users.