https://protomaps.com/docs/faq#openstreetmap
I also maintain open source tooling for anyone to replicate and extract OSM on-demand, as well as a free download portal:
I note that:
> OpenStreetMap ... standard tile layer ... openstreetmap-carto ... is based on dynamic rendering of raster images, instead of vector tiles that can be customized on the client.
so, does OSM really not make vector tiles available? That's too bad.
Basically they want you to host your own tile server using the OSM dataset. There are also commercial offerings that do this for you, but not for free.
Paul Norman has a project called Tilekiln to adapt vector rendering for this use case on OSM.org: https://github.com/pnorman/tilekiln
Openstreetmap doesn't really do a lot for hosting maps for third party websites. You would use Mapbox, maptiler or other suppliers for that and libraries such as mapbox/maplibre, openlayers, leaflet etc. that can render either bitmap or vector maps.
The trick with protomaps is that instead of deploying gazillions of tile files, you upload a huge single file with all the vector content inside and then use lambda functions to extract tiles from that file. And then you use caching and CDNs to to make sure you don't have a lot of compute overhead . So, the API looks like a normal tile server. The data deployment process boils down to uploading a new file and your usage data is a little bit of compute for the tiles your users ask for and a networking cost related to using a CDN.
So, that adds up to a lot of savings potentially. At least, as long as commercial providers don't lower their cost. Obviously, they are free to do similar things technically.