On macOS, it’s possible to schedule repeated shortcut runs using Calendar. The idea is to use Bear’s export action with the markdown option.
The tricky part is having this done for all the notes or creating a folder for each tag, because Bear doesn’t have an action returning all those entities. If you already know the tags you want to export, you can use search’s tags syntax and export each of the returning notes into the destination folder.
Alternatively, you can use the backup action, uncompress the archive once saved, and extract the MD files.
Feels like the backup action might be the most straightforward approach. I tried building a process using AI but it started getting really finicky around the shortcut actions