It seems to happen with both the first and second levels. I haven't progressed any further due to the glitch.
As for the browser console, please see here: https://pastebin.com/wG5DSkje
Hmmm. Looking through the console output, I don't see any errors being thrown from the game. For why it's freezing,it's probably lines 15-17, but those JS files aren't from the game and I'm not sure where they're coming from. Since you tried it in multiple browsers it doesn't seem likely that it's an extension. It could be a network problem, I know Itch has quite a few problems with VPNs if you're using one of those.
You might try to use the offline version and see if that resolves your issue, although it's not the easiest thing in the world to set up.
Just a quick heads up, if you were using a controller at the time you had these issues, the most recent patch may have fixed the issue. Given how fiddly the web controller API can be, it would explain why the issue only happened sometimes. If not, then I'll keep my eyes open for more potential causes.