@Jules999
There are rules about who can enroll in NHIF (because it really is a fab deal), and I believe that non-EU citizens are excluded if they're retired or otherwise "economically inactive". However, it's no problem to enroll if you're employed or self-employed (and, once enrolled, if you cease working you can register as unemployed and continue to make contributions). Brits who got residence prior to Brexit (before end of 2020) received 5 years residence permits, and are treated as EU citizens by NHIF. Hence you can enroll as unemployed immediately.
Enrolling is not super difficult, and doesn't require lots of paperwork. It's a government office, so it usually goes easier if you take a translator along with you. You just go along to your nearest NHIF/NRA office and tell them you want to start making contributions.
My recollection of the process is a bit hazy, but it's based on your 10-digit ID number on your residence permit. By default, this is not "active", so there was one form to be filled/signed to activate it. And then a different form/person to register as unemployed and start making contributions. Sometimes, they want confirmation of when you became a legal resident (even though the date is on your card). So this means a trip back to your immigration office where you ask for the confirmation letter for NHIF (which normally requires a small fee, and returning in a few days to pick it up). So it can take 2 visits to NHIF.
While at NHIF, you should also ask for your PIN for online access, so you can make contributions online. When you're registering, and ready to start making contributions, you should pay some months immediately (they take credit/debit cards). This is so that you have immediate cover (not sure if the magic number is 3 or 6). The easiest is probably to pay for a year, and then go back to the same office every year. Or, pay online.
This online system allows a GP/hospital (or you) to check your ID number for coverage. It says "THE PERSON HAS CONTINUOUS HEALTH INSURANCE RIGHTS". Or something else, not useful (except for you, as you rush back to NHIF and pay more money or ask them what's wrong). If you've got cover, everybody's happy.
Try it, this is the link. Select LNC as your ID type, and enter your 10 digit number, and your date of birth. (Checking doesn't need a PIN, but paying does.)
https://portal.nra.bg/health-status
The next step is to find yourself a convenient GP. Many (most?) don't speak English, so you might have to shop around, if your Bulgarian isn't much cop. You probably can use your phone and Google Translate, but things are a bit easier if they do speak some English. We're mostly in Plovdiv, so we've found a great GP (and dentist) who speaks good English. It might be a bit harder if you're out in the sticks. Our house is out in the sticks, so it might be a bit of extra aggravation if I got sick out there... but so far, I just wait until I get back to Plovdiv. You don't have to register with your nearest GP, so it's OK to register with one in another village, or your nearest big town.
The last step is, once you have full coverage, you go to the appropriate office (I think it's still DSK bank, or maybe it's all banks) and ask for your Bulgarian EHICs. These will give you cover elsewhere in Europe. (I think, if you're covered by the Withdrawal Agreement, that you can still get UK EHICs. I don't know, as I didn't try to get one.)
Even if you have a GP, nothing stops you from going to another doctor/specialist elsewhere (in a PRIVATE hospital). But then you pay (typically 25-150 for a consult). Public hospitals work like the NHS, you need a referral from your GP, you can't just rock up expecting them to give you a knee replacement. :-) Both public and private hospitals have emergency departments, so these don't need your GP involved. I go to the private hospitals as they have few people waiting, and they have more English speakers. My guess is that a public emergency ward is just as crowded and unpleasant as an NHS one. :-)
The whole public/private thing is very unusual. There is no equivalent in the UK, you either use the overloaded NHS and spend a lot of time waiting, or you go to your local BUPA hospital and pay the full private price. One of the unexpected benefits/pleasures of Bulgaria is being able to indulge in private treatment for minimal cost. But, having said that, our village friends (up near VT), are registered with their village GP (speaks English) and are 100% public. They tell me that their experience has been far better than the NHS and they've got what whatever they needed very quickly and very inexpensively.
Fortunately, like you, I'm in tip-top health, so I haven't really needed anything. But it's very reassuring to know that I've got it, and I know how the system works. I've also been a lot more proactive here in terms of checking my health, whereas my years in the UK/NHS was strictly in response to being sick, with minimal preventative care (mostly just my shots and my regular dentist visits).