You can try with the latest FAF production release:
https://github.com/FAForever/downlords-faf-client/releases/download/v2023.8.0/faf_windows-x64_2023_8_0.exe
If it does not work, for whatever reason - try the alpha client, which is in public testing phase right now to mitigate the DDOS. It has some bugs, like non-working country flags, but at least you should be able to login and play online again.
https://github.com/FAForever/downlords-faf-client/releases/download/v2023.10.0-alpha-1/faf_windows-x64_2023_10_0-alpha-1.exe
If both options do not work, then check security settings and change your default browser just to narrow down the issue.
