@CarlS1986
Typically, residence permit applications require that you meet certain conditions in order to qualify. Common options might be work related (self-employed in some capacity, or with a formal employment offer), or retirement related (you're older and you have a pension). When you have a job elsewher or you're too lazy/rich to work (i.e. you don't need the right to work in the country) you would need an option for folks of "independent means".
Not every country has such a visa/residence option. Bulgaria's is the "investor" option for the D visa which requires a 300k euros investment (which can be in property, including one to live in and/or units to rent out). Spain's is the NLV (No Lucrativa Visa) which requires 2.5k euros in monthly passive income, or 30k euros in savings. Portugal has the popular D7 which is similar to the NLV.
As well as the financial requirements, you typically have to have health cover, and a place to live. Thus, immigration wants to see proof of your finances, proof of health insurance, proof of address (a deed or long term rental contract).
They don't usually question you about how long you're going to stay, so your plans for part-time residence are immaterial. However, most residence options do have some minimum stay requirements and you'd have to observe them or risk losing your residence status. Some might be 6 months or more per year, but most have shorter minimums. In most places, 4 months annually would be plenty (and you might be able to get away with significantly less).
While most folks get residence permits for a country they plan to live in full-time, and indefinitely, it's not required. As @JimJ indicates, your preference is not typical, but it can happen. Some people might want a fancy holiday villa on the beach in Spain, and be free to stay there for long holidays if they want to (rather than being restricted to 90 days, with a 90 days break, per Schengen rules). Or maybe they plan to retire there later in 10 or 20 years. Some people might be working in a high-cost but high salary country (like Germany), but want to retire to a low-cost country (like Bulgaria or Thailand). Some people (perhaps like you) might earn a fancy offshore or remote worker salary, and might like to have official residence in a low tax jurisdiction (such as Bulgaria, with 10% flat tax). Some might be non-EU citizens (such as Brits) who feel (as I do) that it's extremely useful to have legal residence somewhere in the EU. Especially as there are clear pathways to permanent residence, an EU passport, and access to/portability of public health coverage. (After 5 years of legal residence you qualify for PR status which is pretty much indefinite, and very hard to lose, even if you spend considerable time away. After that, you can potentially qualify for your passport.)
I have a legal residence in Bulgaria, and I have a permanent residence permit. However, I still have my residence permits for both Cyprus and Spain. Originally, I would have said that Bulgaria can't compete with either of these countries which are (deservedly) very popular tourist and retirement destinations. However, Bulgaria has really grown on me, and it's certainly far cheaper for property purchase, living costs and health care coverage. Consequently, I now spend most of my time in Bulgaria, and just a few days/weeks in Cyprus and Spain. That's so little, I could equally visit with my 90 days visa-free per my UK passport. But I like having my permits, and being able to go any time I want and to stay as long as I want. After all, I might change my mind and decide to spend a year in our Spanish apartment to brush up my Spanish rather than treating it as a holiday flat. (My Brazilian partner already spent a lot more time there than me, and she recently got her Spanish passport.) As you can see, there's no legal barrier to having multiple residence permits, and with annual visits I'm in no danger of losing either of these permits. (On the other hand, I also had Panama and Chile residence permits, but my long absence would mean they were no longer valid, even if I had returned before they expired.)