Did you manage to fix it? I have the same issue...
Greetings. Ever since this latest season released, I haven't experienced this issue. However, I do have a remedy that worked for me back when I was experiencing this.
When you've finished matchmaking and are being loaded into the match, the loading screen will be black with the Apex Legends animated loading icon in the bottom right of the screen. If this screen stays like this for longer than 2 seconds, then it likely means that you are not being connected to the match and it will eventually kick you back to the main menu or lobby.
What you need to do is... As soon as you see that the black loading screen is staying there for longer than 2 seconds, quickly switch back (Alt-Tab) to your Cloudflare WARP Client and turn it off, temporarily.
What will happen is, the moment you turn off your WARP connection, the black loading screen will leave and the game should show your loading screen wallpaper and/or then continue to the pre-match screen where it waits for other players/teammates to connect to the match. Once you see this pre-match loading screen, it is now safe to turn your Cloudflare WARP back on.
Try not to do this maneuver too quickly or else it won't work but the timing could come down to hardware differences so you might just have to give it a few tries until you figure out what works for you. I won't go as far as to say that this method is guaranteed to work for you but it worked for me and I hope that it does the same for you.
