It's a common misconception that the OpenStreetMap project provides free map tile resources for use by others. The focus of the project is the map data.
What is the misconception? That paged you linked to says that map tiles are free for use with a few reasonable restrictions:
Clearly display license attribution, normally in the bottom-right corner of the map.
Do not actively or passively encourage copyright infringement.
Recommended: Do not hardcode any URL to tile.openstreetmap.org as doing so will limit your ability to react if the service is disrupted or blocked. In particular, switching should be possible without requiring a software update.
Recommended: add a link to https://www.openstreetmap.org/fixthemap to allow your users to report and fix problems in our data.
Recommended: a contact email on your web page or app store page. If we cannot find contact information we will be unable to do anything except block if an issue arises.
Of course, there is no Service Level Agreement:
Although our map tiles are generally very reliable, their availability to others is on a best effort basis and we offer no SLA or guarantees.
But that seems quite reasonable for donated resources.
Pretty sure I am not paying anything or using any API key :) Open Street Map basemap was too colorful and contrast with my color scheme was not very good in many parts of the map
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]
From what I can find, CARTO does not have a free map tile server. In other words, while it technically works, I think it's against their terms of service. They probably don't care if you're small, so I wouldn't worry about legal threats, but at some point the tile server might check the referer and break your app.
https://operations.osmfoundation.org/policies/tiles/