MWAA WebLoginToken auth randomly fails

I'm using MWAA with Airflow 2.2, private network access mode. I'm trying to log in using a token generated through boto3. My role has Admin privileges in Airflow. The URL I'm using looks like: https://<HOST>/aws_mwaa/aws-console-sso?login=true#<TOKEN>, just as recommended in the docs.

The issue is that the generated URL does not always directs me to the Airflow home page, seemingly randomly it ends up redirecting me to the Login page using the following URL: https://<HOST>/aws_mwaa/aws-console-sso?next=https%3A%2F%2F<HOST>%2Fhome. Using the same login URL with the same token it sometimes works, sometimes doesn't. Looking at the Network traffic it shows that the Login page redirects to the /home endpoint as it should, but it receives 302 instead of 200 and directs back to /aws_mwaa/aws-console-sso. Again, this happens randomly, in ~30% of the times when I want to open the Airflow UI this way.

I'm using MacOS Monterey 12.4 and Chrome Version 103.0.5060.134 (Official Build) (arm64). I could not reproduce the issue on Safari, apparently the login always works there.