Gave it a listen—I'd call it G minor, which is the relative minor of B♭ major, so it has the same key signature of two flats (meaning you're not wrong in a sense!) except with G as the tonic ("home" note) instead of B♭. The way to suss it out is to figure out what note feels like "home" or "at rest." If you continuously play a B♭ over the chord progression, you'll hear that it's pulling down, and if you follow that tug down the scale to G, you'll hear that it feels at rest, so you can just keep playing G over and over and it won't need to move anywhere. Another hint that it might be G minor is that the opening chord is G minor and the opening melody note is G. That doesn't guarantee anything, but starting on the tonic chord is pretty common, and the most conventional notes to start a melody on are probably the first and fifth scale degrees.

One thing that might've led you to B♭ major is how in the middle ~third of the song a new motif is introduced which IS in B♭ major. I think it would be fair to call this section B♭ major; if you try that same trick again, you'll notice that G no longer feels like home, while B♭ does. In fact, returning to that hint about melody scale degrees, the melody starts out by walking up the B♭ major scale from the first degree (B♭) up to the fifth degree (F)—again, not a given, but something to listen for! After that motif goes away, it returns to G minor, which is why I'd feel confident in calling it G minor overall.

It's always fun to just vibe out and jam to a nice chord progression! A favorite of mine is the Grover Washington & Bill Withers classic "Just the Two of Us" (the recording is maddeningly a bit sharp from A=440 Hz, but thankfully you can usually compensate for that on an electric piano). Besides being a great progression in and of itself, it's also pretty handy to learn because it's a chord progression you hear all over the place; three examples off the top of my head are "My Boo" by Ghost Town DJs, "Moonlight Sunrise" by TWICE, and the main theme from Spirited Away, "One Summer's Day" by Joe Hisaishi (yes, seriously...if you focus on the bass line of the "chorus" it should help to hear it!).