UKH

I'd like a small, cheap smart(ish)watch for swimming, that let's me time my efforts, and let's me control podcasts that it sends to some earbuds.

Does such a device exist? 

And do you like smartwatches in general, or are they overpriced toys. 

I don't think bluetooth between watch and earbuds is going to work very well when your wrist keeps going underwater.

I’ve heard good things about the Garmin Forerunner range, which I think you can install Spotify on.  
If the music element isn’t a dealbreaker, I’ve been really happy with my Polar Vantage M. Reasonably priced and it’ll record data for any activity you want it to. 
 

The music requirement will generally push you into the higher end of the smartwatch market. Cheap watch with music might well require going second hand, depending on your personal definition of cheap.

Might be better with a cheap watch for timing and waterproof headphones with storage for podcasts/music. The only way a Forerunner or similar is going to stream podcasts to earbuds etc when swimming is if you keep your head above water and keep the watch in your swimming cap (at which point you won't be able to use it to control the earbuds). I suppose if you strapped the watch on a tow-float you could maybe stop to fiddle with the music controls on the watch.

Are you swimming outdoors or in a pool? I just track on Strava on my phone, and that goes in my tow float. You could also have a playlist set up on your phone too. However, if you are in a pool, the tow float might look odd! 😂

In a pool. 

So it looks like a cheap watch and an mp3 playing headset might be the way to go for me.

Any recommendations for waterproof headphones?