Thanks for reaching out about this here in the Community.
If your Spotify app is updated to the latest version and youFilter-search something in your Liked Songs to play it, the playback will keep going after the selected song is finished only if the result of your filter-search is a list of songs.
For example, if you search the word 'heart' in your Liked Songs and are able to display 6 songs as a result, then the playback will continue across all the remaining songs in the list after you play the first one. Correspondingly, if the result of this search is only one song then the playback will stop after that one song is finished.
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