You’ve had some other recommendations already but I’d suggest also looking into FlatGeobuf [0] for this use case. Have a look at the MapLibre example with a 12GB example [1]. You don’t need a server at all (unlike MBTiles) and will be able to load far more points at once than your current solution. Can easily generate it with QGIS/GDAL/PostGIS. Not sure what your plans are for the project but would be happy to donate some time to get something like that working.

[0] https://github.com/flatgeobuf/flatgeobuf

[1] https://flatgeobuf.org/examples/maplibre/large.html