Hey ayocado, I have some experience with self-managed/self-hosted base maps. There are some modern tools that make the setup pretty easy (e.g. Protomaps, MapLibre) and you can still use a minimalist style similar to the CARTO one you have now.
If you're interested in switching over, feel free to shoot me an email and I can try to help!
Here are some demos [1][2] I've made without using any third-party map services. All open source! [3]