Is there any use to mushroom blocks in Minecraft JE?

"Other than"? Not really. Source of mushrooms when broken by non-silktouch tool.

Mushroom stems are considered a very valuable decorative block, going well with quartz. Also, the chance of rising compost level in composter by 1 is 85%, one of highest available, so if you want to discard them, running them through an automatic composter setup would be preferable to dumping them into lava.

Ability to insta-mine them with unenchanted iron axe, while still taking time with a pick, makes them a good scaffolding block - removing them with an axe keeps most of the built structure safe from being mined accidentally, while correcting mistakes in the build rarely risks damaging the scaffolding.

One interesting, though rarely useful property they have is changing block state permanently when another mushroom block of the same type is placed adjacent to a side - the block's texture on the side of contact changes (to "inside" of the mushroom) and stays that way after the other block is removed. This state change is noticeable using observers and could be used to detect exceptional states like arrival of a particular segment of a flying machine.

There's one more important use for them for technical players, although not in the harvested block form - the giant red mushroom's 'skirt' part has the property of replacing (destroying) any non-full block that it happens to overlap when the giant mushroom is grown (e.g. by bonemealing a small red mushroom planted on a mycelium/podzol block). This is an easy way to remove a part of the portal frame of an End portal, making it possible to exploit it as a gravity block duper.