@HelenDinBG and @janemulberry have already posted some great advice for you.
Unfortunately, there isn't yet a Digital Nomad visa in Bulgaria.
There is in our neighbour Serbia though, and it's getting great reviews in nomad circles.
https://www.supportadventure.com/serbia … mote-work/
Serbia is another Balkan country, with similar culture, food, climate and cost of living to Bulgaria. So I think it's real alternative. Especially as it doesn't just have a visa for nomads... it also grants residence permits for either purchasing a property (no minimum) or incorporating a Serbian company (with corporate bank account).
It's an easy drive to Bulgaria, so you could potentially be resident there, but travel regularly while renovating your Bulgarian pad... and figuring out how to get your Bulgarian residence permit.
As you're already freelancing, it would be quite straightforward to get your Serbian company (and hence your Serbian residence permit), and put your freelance work through it. In 2 years (perhaps less if you incorporated before end of 2021, as I think it might be calendar years) you'll have enough history to get the Bulgarian TRO (Trade Representative Office), which gets you the D visa... and then residence.
Alternatively, there is a freelance visa in Bulgaria. If you plan to live here full-time, and learn Bulgarian... then simply come here for a couple of months and learn Bulgarian first. When you pass the B2 test, you can get the work authorization... and hence the D visa... then residence.
Language schools do intensive classes at different levels/duration. I reckon a month intensive for beginners will give you a great foundation. Then a second month intensive for intermediates should get you to B2 (and probably the necessary certificate). It's probably around 1,500 euros per month for a language school (less if you find a tutor). This is a good way to see a bit of the country too. And renewals will be easier as you already speak the language.
As there's a company already in the family, you could, indeed, use that. Location of the company doesn't matter. It just needs to be a corporate entity with 2 years of history. The level of turnover is not important either, you just need some summary accounts. Most importantly, you need to show the company is in "good standing" (many places issue a formal certificate to this effect). This means that the registration is still current, that all filing/corporate fees are paid up to date, and that you've properly filed/paid taxes (based on the accounts).
Personally, I'd prefer to have full control via my own new Serbian company. But if you're on good terms with your sister and happy to go this route, this would certainly be quicker. The TRO is a registration with the Bulgarian Chamber of Commerce. This would be for your sister's company in Cape Verde. And, effectively, it belongs to her/her company. As she has (I'd guess) no interest in living in Bulgaria, she could nominate you to represent her/the TRO here. There's some formal corporate paperwork for this, I'm sure.
The TRO registration for the company + your nomination as the representative will be grounds for issuing the D visa... which then gets your residence. Once you have residence, you can do "family reunification" to get your partner's residence.
The TRO requirements are a bit of a faff, as they need corporate documents (issued in Cape Verde)... and needs lots of authentication/legalization and certified translations. Plus your formal application for the TRO. I'd recommend paying an attorney to guide your through this (probably gonna be less than 2k euros).
I think this way you get 1 year residence permits (maybe 2). So you'll need to keep everything current for a few years and do multiple renewals until you make it to 5 years. Then you get permanent residence, and you can relax.
You should note that only one of you needs to jump the extra hurdles (proficiency in Bulgarian, or TRO, leading to D visa) required to get residence. The family reunification process is just a formality (proof of the family connection to existing resident). You should also note that the first residence permits are "temporary" ones, so you must keep renewing until you make it to 5 years. Your "long term" (or permanent) residence is a big milestone. It's (a) harder to lose, and (b) gives you many of the rights of EU passport holders (specifically freedom of movement in the EU).
Separately: the Bulgarian minimum salary is about 300 euros per month, or 600 euros for two. With an income of £3-4k you could live very comfortably. Plus, good connectivity: my village has fiber internet to my house, so my wifi is around 75mbps. That's 10 euros/month, plus my last leccy bill was 20 euros.
£15-20k in savings is not a massive nest-egg, and Bulgarian property prices are rising. In my village, that wouldn't even buy the plot of land. But if you're flexible about location and shop carefully, you certainly should be able to find a decent village house with a large garden that you can renovate. There are also some interesting pay-monthly village properties (see Ebay) that could stretch your budget further. Bulgarianproperties (dotcom) has loads of listings all over Bulgaria, so for a bit of research just enter your max price, and review the results.
As extra faff, the non-EU issue means that: (a) you'll have to buy your village house via a BG company (apartments without land OK in personal names), and (b) importing your UK vehicle will require you to pay VAT + duty (so if it's a fancy motorhome that will be a chunk o' change).