Hi, I have the same problem trying to link to BG Home.
I don’t know if anyone solved the problem in this thread, but if it helps I just had the same issue.
I found that it was caused by a glitch with the last device I added to Smartthings. I don’t know why, but I had to remove it and as soon as I did the connection to Google worked again after I reconnected the account. I then added the device back and all was ok.
If you don’t know what the problem device is I realised it because the Alexa app could control everything on Smartthings except that one device.
Hopefully this helps.
If it happened today, 13th June 2023, the timing of your adding a new device was probably coincidental. It was almost certainly caused by an Internetwide outage involving both Google and Alexa, but variably for different people. See the existing discussion:
Amazon Web Services Outage affecting many integrations 13 June 2023
Thanks. Interesting. Could be. I guess we’ll never know. 
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Thank you, work to me!!!