Is cobra health insurance allowed when you have another employer’s plan?

My old job’s insurance covered more than my new insurance which is now HDHP.

I had deductible met under old plan and 10% instead of 20% coinsurance. There was a medical equipment order sent by doctor while I was still under old plan but it may take a few weeks until I get it from contracted their equipment vendor (for sleep apnea)

Doing research, some sources say that once you get new employer sponsored insurance, you can’t continue with COBRA, others say coordination of benefits is pain and most likely new employer’s plan will be primary. I estimated if I get this order soon within next 30 days, I would benefit more through through COBRA coverage especially if my new plan with high deductible renews in January, but if I had to pay for cobra premium second month or more then I am better paying cash under new plan. What makes it trickier to understand my new employer health plan is HDHP which start on my first day of job this month and contributions for HSA start next month while my old plan was shared deductible plan that did not qualify for HSA.

Are the rules say or different for Dental? Suppose my new dental is Basic PPO and my old was Enhanced PPO that may cover more.