How naive a person needs to be to hope that the tax office of another country will not notice the purchase of real estate by a foreign citizen and will not ask his source of financing.
Georgia is a very good country with a good climate, but in order to live there, you need to take into account many nuances. Therefore, I always advise legalizing income through a business in your country.
If they allow foreigners to purchase properties, then don't have any interest in checking how did they get the funds, as any taxes would be payable in other jurisdictions anyway, so nothing to gain for them.
Not to mention they don't have any authority to launch any routine investigations in foreign countries, so even if they asked you for the source of funds, they'd probably accept any answer. So not sure how do you imagine the process would look like? Do you think they'd auto-appoint a financial forensic investigator for every house sale?
Again, we're talking about purchasing with fiat with a fiat bank transfer from abroad.
Between the countries there are treaties on tax control. Nobody will prevent you from buying a house or other real estate, because you are making investments in the country.
And after the purchase, the tax office has several years or more to check the legality of your funds with which you bought the house.
If there is no such procedure today, this does not mean that next year it will be the same.