I've considered them to be a subset of fungi in the group 'polypore'
Some of those in the group grow like fronds off of the sides of trees, stumps, and have that sort of stripy look when from head on. They don't generally grow with moss but I've really just seen it as a design choice more than anything, (to really signify the overgrown, old mossy feel).
Where I live (same overarching biome as where CA most likely got the inspiration from - same mossy trees often too), I most often come into contact with 'spectacular polypores'
(you can see the mossy, dead, what looks like douglas fir they're growing on)
Though they don't look too similar to the in game variant and generally grow on nursery logs (fallen or dead upright trees which home many insets, bacteria, fungi, plant life, and even animal life). I do often see them on the sides of lower parts of evergreens like douglas fir with it's relatively thicker, moisture-capturing bark.
There are however polypores which grow on the sides of living trees more often. I can think of the 'Hemlock varnish shelf', 'Birch Polypore', some turkeytail mushrooms (which look rather similar when head on, being remarkably thin)
(ganoderma genus polypore, looks very very similar but grows in an entirely different climate than my own)
(unnamed 'shelf' polypore)
(turkeytail, pretty easy to imagine how they'd look from the side, and growing amidst moss, even if not really inside of it)
Hoped you enjoyed my little fungi rant, I find it quite interesting to trace back the inspiration of stuff in the game to where it may have come from, especially from someone living in and around basically the same general environment as SDV is set within