Welcome to TRT Nkhxn, and sorry for missing the welcome wagon earlier.
And you posted in the perfect spot for this question......and YES, you have a 'Mushroom coral'. But now what kind is the hard part. This category of 'corals' are seemingly always in flux, getting renamed/categorized/classified.....just a quick look to help ID this morning, I see some are even referred to as 'fake corals' now.
Just from the picture I'm gonna say it's a Rhodactis Mushroom....
There are different types of mushroom corals for reef tanks. The types are Discosoma, Rhodactis, and Ricordea Mushrooms
saltwatercoraltank.com
Nothing at all wrong with leaving corals on their base they come on, other than for personal aesthetics, and they will eventually cover them. I personally never remove them.....lazy is probably my excuse.

Lower flow is always a safe bet with mushrooms, though enough to keep dirt off them to save you the work of having to blow them off(See my lazy excuse above). Lighting......anywhere from way down there to way up there seems to work. But starting low, then GRADUALLY moving up in PAR is a safe route. No need to blast them in light if you have options, but will adapt most of the time.
Hope the hobby treats you well, and ask away with any questions,
Hack