Is it a requirement to register with GP

You don't have to register if you have private medical insurance and you can go and visit a GP of your choice whenever you want to (find one near to you on Superdoc). If your insurance doesn't cover GP visits you pay a pretty small fee to the GP.  If you're a pensioner you can get an S1 from whichever country is paying you a pension and then register with NHIF, which entitles you to the same treatment as a Bulgarian pensioner (which frankly is nothing to write home about). You'd be wise to either retain your insurance or keep a decent-sized "rainy-day fund" handy, to give you the flexibility to make any necessary but optional medical choices that cost extra (there's no shortage of Lancelot Spratts that you'll be happy to pay to avoid here).

It would be worth considering paying into the public system - I certainly do.  Reason being, not only will you get treated at public hospitals, but you can often get treated at private ones too, depending on your condition and where you live.

If the area you live doesn't have a relevant treatment available to you, then you can ask to go to a private hospital. Inouve in Varna and in 2023, I was seriously ill, with a gastroenterologist problem. The consultant in Varna said she didn't recommend getting treated in Varna and refered me to the Heart and Brain Hospital in Burgas, that has a gastrointestinal unit.  It was an amazing hospital - absolutely brand new and spotlessly clean, you could eat your dinner off the floor. All I paid for was the room - at the time, 75 leva for three nights. I had an endoscopy, ultrasound and MRI.

To register on the public system, you have to first register with a public GP, who will give you documents to take to the NRA office to get registered. You can pay monthly, or in one hit, for the whole year, by card or cash.

As for public hospitals, they're generally pretty run down, but in the bigger cities, usually well equipped with modern diagnostics. I've used the Military Hospital in Varna, very close to where I live and I was certainly happy with my treatment - the doctors, nurses and staff were all great, although, of course, some don't speak English, so Google Translate was very useful.