... to find the insurance from the next company doesn't recognize "you could have paid for COBRA" as continuous coverage which means they won't cover preexisting conditions for at least a year.
Most companies, in my experience, are "group health plans" and never really considered pre-existing conditions or cared about a break in health insurance.
Dental plans, on the other hand, don't even care that you had COBRA. I went from a Cisco provided MetLife dental plan where I had a tooth extracted in preparation for getting an implant put in. Before the extraction site could heal, Cisco laid me off and I had the implant socket? put in place under COBRA, which was effectively still Cisco's group plan. Then I started a new job and signed up for their insurance benefits and kept my COBRA benefits until the end of the year when the deductibles reset. In Jan, I tried to get the tooth put in (the implant crown) and the new employer's MetLife dental plan said they didn't cover "missing teeth". Because the "group plan" changed, regardless of being a plan through MetLife, and having uninterrupted coverage, it was still considered a missing tooth and I had to pay the full cost of the crown.