You should buy the web version if you want both. Web version comes a Steam key.

Does this still stand? as I'd like to play the premium of both versions.
EDIT: No, it's not a thing, just bought it twice...
Be nice if the dev updated info on the website regarding this making it crystal clear it does not work both ways with either purchase.

This. It's not a deal-breaker for me, but I would have bought the web version first if I had known.

No - you have to buy it separately, per my review.

Buy the web version, which will give you a Steam Key - which is what I should've done. I bought the full version after (too late to refund the steam version).

Update: You do need to buy both versions for Browser and Steam. Players that owned the game before the Steam release got a code for Steam or the mobile port still in development. If you are subscribed to the top Patreon tier you can get both though.

Honestly it's pretty ♥♥♥♥♥♥ that they don't still just give you access to both. It's put me off purchasing either title as I'm not paying twice when folks who came before didn't.