I am more interested in the music being played in Williamson's car right before he is taken away and killed.

Is is the country music in this scene "What are you doing in my car?" "Waiting for you." "Get yourself killed that way." "Or the reverse. Get out, Beau" or the piano concerto as Elliot is driving through the gates of Williamson Ranch?

I don't know the song titles but it sounds a lot like Bob Wills & His Texas Playboys.

Well, when Columbo takes out the cassette, it can be read: "Tennessee Ernie Ford - Songs I like to sing". I couldn't find the album either on Spotify or Apple Music, but as I saw, the vinyl (or the cassette) can be bought on Discogs, Amazon and eBay.