COBRA is when you are laid off of work; it extends your coverage up to 18 months as long as you pay the full cost of the plan, both your share and the employer share.
Since you quit, it’s entirely possible that the employer is getting ready to change insurance carriers. Since you are not an employee who will be enrolling in the new plan with the new carrier, they offering you a Portability plan, which is new insurance that you can enroll in that has a 6 month look back period for pre-existing conditions, as opposed to 12 or 18 months. Almost all states have what’s called a “pre-existing condition exclusion clause” for all products (some states exempt HMO plans from pre-ex). If you were to get a new job and be added to a plan at the new employer, you would be subject to pre-ex unless you could show continuity of coverage from the time you left your old employer. If you were to start a new job, and got new coverage, and developed cancer 3 months after starting the job, you would not be covered if your new plan had a pre-ex clause.
The other option is a conversion plan, which is state mandated insurance. They should offer you that as well.