Adding one more workaround that isn't mentioned above. In my case, the existing 401-error fixes (incognito, official link, contact support) didn't help. What finally worked: signing up with a Gmail address that has no dots.

Gmail treats first.last@gmail.com and firstlast@gmail.com as the same inbox, but Databricks' signup seems to strip special characters and store the result as the username (this is an assumption). If you had any earlier failed attempts with the dotted version, a ghost account exists for the dotless one too, and new attempts fail silently.

Fix: incognito window + same Gmail without dots = signup went through on first try.

Hope this saves someone the troubleshooting time.