How does one tag a facility that is used to take water from a river (through filters) into an industrial facility?
If it is not a pumping station there must be some kind of inlet into a channel or a pipeline. You will find some general information on the wiki pages
Water management - OpenStreetMap Wiki
Key:inlet - OpenStreetMap Wiki
When there is an inlet you can map, the most simple thing would be to add a tag like inlet:filter=yes. If the filter is incorporated in a kind of building or else you better post a picture of this object to make clear what we are talking about.
Edit:
I can see the inlet from the river into the “filtering” plant. There is a weir to the left of the building to grant permanent water supply. I would tag the inlet itself as described on the wiki page and the area of the 2 buildings with man_made=water_works (which is for all kind of water treatment plants according to the wiki) and probably add water_works=filtering_plant. The 2 buildings should go with building=service.