Ideas
I'm gonna chime in here, I'm also having the same issue. During the past weeks, on that infinite loading screen, it would occasionally prompt me to sign in because "Apex Legends requires and EA account" or whatever bs it says. Once I sign in to my EA account and even click "Remember this device", when I close the game and open it again, same issue happens.
Now, when it did had me sign in, on my EA account, under "Linked devices", my PC would should up each time I had to sign in, even though I'm using the same PC, just the one, it shows up as a different device. At one point I had over 15 devices, "FIFTEEN"! BUT it was all just one device, my PC.
Up until about 3 days ago, I stopped getting that prompt to sign in, and I'm just stuck looking at that **bleep** infinite loading screen.
Tried reaching out to EA, nothing, did most of the steps you did, still nothing...
I also tried Apex on a different account, same thing again...infinite loading screen and never prompts me to sign in anymore.