Google announce the end of the ability to sign in with Google from within applications, nearly two years ago. It took until early this year for it to really be turned off, but SketchUp was made ready for that to happen, with the SketchUp 2019.3 version.
At that point, instead of signing in from within SketchUp, you now get given a web page instead. Anyone using SketchUp 2019.3 or later can continue to sign in with Google. Anyone using 2019.2 or earlier will need to sign in with a Trimble ID.
If there is any chance you have a 2019 license, you could make sure that you are on 2019.3, and then you can continue to sign in with Google. If not, the next challenge becomes getting the Trimble ID going.
I can see that you have tried a few times. I just had a new password reset email sent to you, look for a new message, that arrived maybe 5 minutes ago. Try using the link in that email.
When choosing a password, try to keep the number of special characters down to one. There is an issue we’re looking into where if you chose two or more special characters it can make the password reset page fail.
Assuming you get further, with the new password reset and the change of a password to include only one special character, do a test sign in on sketchup.com. If the sign in works ok there, it should work from within SketchUp as well.
edit: Of course, I made a start of year error there, not quite used to it being 2021 already. Google turned off the ability to sign in with Google from inside applications, in early 2020.