I went to England for a buddies trip in March 2020 to catch a few EPL games, and we were able to see Chelsea in the last game before the pandemic shut everything down. Compared to trying to get Liverpool tickets (the only 2 out of our group of 5 that went to that game had a $$$$ hospitality package), getting Chelsea tickets was relatively simple. Now, granted, this was almost three years ago, so the procedures might have changed, but here's what I remember:
We all needed to purchase memberships to the Chelsea fan club in order to purchase tickets (I think it was like $40 a piece). Tickets went on sale a little over a month before the game, I was up at 2 am ET in a queue to purchase them and was able to do so no problem, despite not having any Chelsea loyalty points. Having a fan membership also got you access to the Chelsea ticket exchange, where tickets for the game also popped up at various points throughout the following weeks.
Again, after COVID and with the new ownership, I don't know if anything is different now than it was in 2020, but like I said it really wasn't bad compared to the nightmare of trying to go to Anfield.