I'm sorry you're running into this.

Could you try running prefect-cloud login --key <key>(note the - in prefect-cloud) and see if that works instead? Additionally would you mind sharing your browser version?

In case that doesn't work here are some other workarounds:
1: Try Chrome (if you're not already)
2: Manually create/edit ~/.prefect/profiles.toml to look like:

active = "prefect-cloud"

[profiles.prefect-cloud]
PREFECT_API_URL = "https://api.prefect.cloud/api/accounts/<your account id>/workspaces/<your workspace id>"
PREFECT_API_KEY = "<your api key>"

3: Use environment variables:

export PREFECT_API_URL="https://api.prefect.cloud/api/accounts/<your account id>/workspaces/<your workspace id>"
export PREFECT_API_KEY="<your api key>"