What time signature is this song in?

Not swing, really. Joe Cocker’s people too the Beatles version, which did swing by the way, or a shuffle really, and converted it into a very slow 12/8. The result feels more like waltz time.

No, he’s right. Cocker took a 4/4 song and turned it into a slow 3. Now, whether it’s 12/8 or 3/4 is up to interpretation, but either way it’s definitely more than just adding a swing.

Yeah, I’d definitely call it either a slow 12/8 or 6/8. And, as you note, the Beatles version definitely has a swing to it. It is not played in straight eighths.

For the OP’s song, I’m getting a bar of 5/4, followed by a bunch of 11/8 bars (2+2+2+2+3) and then I lose interest.

That’s “Unsquare Dance” actually.

I’m actually surprised, as neither are particularly difficult time signatures. Unusual in Western pop? Yes. Difficult? Not really with a little bit of acclimation. But perhaps I’m speaking from a position many decades onward where these time signatures have been more “normalized” for lack of a better term (i.e., they’re not quite “normal,” but not as exotic as they perhaps once were.)