It's also worth looking at the E-Residency in Estonia.
https://www.e-resident.gov.ee/become-an-e-resident/
Working via this route would qualify you as an EU-based contractor, so remote work would become available.
In theory, you could parlay that work into being resident in an EU country, as you could show that were already working within the EU.
Though I don't know anyone who has tried this method, but it's another potential route towards EU residency.
@BillySmith It sounds great, thank you, will take a deeper look!