I’d also very much like to see this feature! The restriction of the GUI clients not able to handle the redirection has also stopped me from using Cloudflare Access.
What could also be an option is that the Bitwarden GUI clients could offer the possibility to manually add HTTP headers that are sent with each request.
For example, Cloudflare Access offers Service Tokens in the form of HTTP Headers that would allow the GUI Clients to bypass the Web-based authentication.
While this might be less secure than if Bitwarden would support the Web-based Authentication (explained by @haneef95), I think it would still be more secure as without because an attacker would have to sniff the HTTP Requests in this network to get the token. And even if the attacker gets the token, he would get as far as what we currently have without the extra authentication, so no loss and probably way easier to implement.