To pay social security, you have to elect to be employed, or self-employed, or unemployed. There is no "crypto trader" option. :-)
So I don't think there's any issue if you decide to be unemployed in Bulgaria, and just pay the minimum social security contributions to be in the health care system.
That means you don't contribute to a pension, you just pay social security. Unemployed is 26 leva per month. Yes, I know, it's absolutely outrageous. :-) For this, you can get a Bulgarian EHIC card (for cover in Europe) and free (or nearly free) medical treatment in Bulgaria (if you should need it, but I think you'll find you prefer to go private and pay a bit extra).
Bulgaria, like other countries, cares if you make a lot of money from invoicing (performing services), because there's a VAT threshold, and they expect you to register and pay VAT.
Bulgaria, like other countries, cares if you receive a pension, or you make huge amounts of money from your trading activity. These are both forms of income, and so they expect you to declare it and pay tax (the 10% income tax) on it.
It's perfectly OK to have gotten rich before you come to Bulgaria, whether it was dot-com, crypto, or London real estate. Savings are not income, and there is no wealth tax here. If you invest your savings in Bulgarian property to live in, no income tax here either (but small property taxes). If you buy Bulgarian property to rent out, then you will generate some rental income to add to your tax return. If you put it in interest-bearing deposit accounts or dividend-paying stocks, then that's additional income for your tax return.
I don't see any issue with you being officially unemployed, and dabbling in stocks. But then I'd wonder (and, I guess, the Bulgarian taxman too, potentially): what are you living on? So there's an income coming from somewhere, and you should declare it. (Unless, lucky you, you got rich already from Bitcoin, so you're using your savings to live on. In which case, obviously that's cool, no income tax to pay.)
If you're actually working (let's say remotely, via that interweb thinggie) then I think you'll have a harder time not registering as self-employed, or forming a Bulgarian company and making yourself an employee.