Same issue here, the problem is logging in with Roon Arc not a browser. Same problem as noted above, so do not understand how “switching browsers” would do anything.
Frankly, this may be sacrilegious to point out, I don’t think Roon Arc has been functional for me for longer than a few days at a time since it was released…great idea but utterly unreliable and glitchy.
I have i7 Roon Rock server, Cat6 hard wired, 1.5 gig up and down fibre, and 5g on the other end…the myriad of issues are entirely software based it seems. And now, suddenly, I cannot even log in with the app.
ARC and the regular mobile remote are using the default web browser for the login dialog. You could try temporarily changing your default browser.
The InvalidRecaptcha error in the past nearly always turned out to be caused by stuff like traffic/cookie/popup blocking extensions in the browser or blocking on the network level (like with Pi-Hole).