You would just call them accessories or fixtures. However you would need to specify them as “plumbing fixtures” or “bathroom fixtures.” This is because generally speaking, “fixtures” can mean the high-hats, the lights, The flooring, etc etc. You may see this when a shop is closing for good in America. “Everything must go, including the fixtures!” It means they are selling everything in the store, even the wiring. They mean literally everything.

Bathroom fixtures would cover the washbasin (GB) / sink (US, but becoming more common in GB) , toilet, shower, bath etc, and possibly also smaller things like towel rails. There is a distinction between 'fixtures' and 'fittings' which is sometimes, but not always, followed. Pipes, drainage and suchlike are 'plumbing'. They are generally 'behind the scenes'. 'Bottle-trap' would certainly count as plumbing, but it's not an everyday term - only plumbers and very enthusiastic DIY folks would know what it was.

NB Neither 'furniture' nor 'equipment' is correct in this context. 'Vanity' only refers to one fixture - it's just a cabinet fitted around a sink/washbasin.

Bathroom vanity

pipes? plumbing. "sink" is only in the kitchen, here. What is a bottle-trap?