Staying on COBRA when starting a new job until end of year?

I live in California, and I currently have already reached my out of pocket max this year on my employer sponsored health insurance plan. I also have multiple single case agreements set up as well. I'm considering leaving my job, but I would then have to start at zero on health insurance payments, paying the new deductible and likely hitting my OOP max by end of year

With the single case agreements too, those could take a month to just process if I don't have to appeal, plus all the delays after that on submitting claims (and having to call to get them fixed often) means that I would likely need a few thousand dollar buffer for the first few months to be able to pay the out-of-network bills while I wait to get the new single case agreements in order and get reimbursed

I saw COBRA is a thing, I know my job does have that as part of their health insurance, and I saw that leaving a job voluntarily is covered by it. If I start a new job, would that impact my eligibility to stay on COBRA? Even if my premiums doubled with COBRA, it would be cheaper overall and save a ton of effort. If I can, I'm thinking of trying to use it to stay on the plan through end of year and then just switching to whatever my next's job health insurance plan would be for 2025

As a side question, would I still be eligible to contribute to my HSA with my current plan under COBRA? Currently it just deducts from my paycheck, so I am unsure how that works with COBRA