How does COBRA work?

Hello all, I am currently 24 (25 in October) and under my parents’ health insurance and have had full coverage for my Crohn’s disease, the treatment of which is 500mg of Inflectra every 8 weeks (~$2500 without insurance I think). This treatment is done through Kaiser Permanente, and I was told that they do not accept any coverage besides what they offer as an HMO.

My employer provides Anthem health insurance, but Kaiser Permanente doesn’t take Anthem. As a result I’ll be looking outside of Kaiser for a new specialist for treatment (if ya’ll know any GI/Crohn’s specialists in LA, let me know!).

My work does open enrollment for plans only in October and plans from open enrollment go into effect the following January 1st. My work considers turning 26 a life event for me to switch to Anthem effective pretty much immediately.

I think Anthem is okay with being on both my parents’ plan and theirs, but Kaiser would not be okay with that if they found out. Would it be a bad idea to be on both and hope Kaiser doesn’t find out?

What I am trying to figure out is if I should switch to Anthem during the upcoming open enrollment and find a specialist that takes Anthem in LA, or if I should stay under my parents’ plan until the day I turn 26. My only concern with the latter is I think my medication needs to be authorized for coverage by my doctor with Anthem, and I have no idea how long that takes on top any other additional effort. If I don’t get my medication every two months, my disease can get really nasty.

If I can get some ideas of what to consider or additional things I should look into, I would really appreciate it. I’m kind of overwhelmed despite 26 being a bit out of the way. Thank you!

Edit: Adding details mentioned by bot

Zip code – not comfortable stating it but city is Los Angeles

Income – 116k – 126k (idk exactly, I’m in process of promotion)