This seems to be dependent on the Android version. My old Samsung phone has Android 10, the new one has Android 12.

Both have the same Samsung Music App V 16.2.27.5 installed.

Only on the Android 12 phone I could find 
> Samsung Music Settings 》Manage Playlists 》Export My Playlists

and

> Samsung Music Settings 》Manage Playlists 》Import Playlists

Settings can be found in the three dots menu (`...`).

The playlists are stored in `*.m3u`format in the internal memory, directory `Music`.