Also Humanitarian Operations are governed by Humanitarian OpenStreetMap Team [0] - they have their custom styling [1].

[0] https://www.hotosm.org/ [1] https://wiki.openstreetmap.org/wiki/Humanitarian_map_style

"governed" probably isn't the right word. HOT is a separate organization from OpenStreetMap. They do a lot of work editing OSM and there are people with overlapping involvement.

In addition to running their own tileserver, they also often produce large format maps in QGIS or what not.

Only the default style has this; switching styles is literally one click.

Any company or institution that relies on OSM tiles heavily are caching them anyways because the request cap isn't that high.

Or they are running their own tileserver, generating their own map tiles, from their own local database (this is exactly what openstreetmap.de is doing), and would not be affected by this at all.