I believe they are legal, but I would be hard-pressed to point at a specific section of the Firearm Act that directly states it.
Since adapters are not firearms in themselves, a lawful firearm plus the adapter takes on the legal status of the base firearm
as far as firing it goes would be my opinion.
You may run afoul of range regulations, since there are safety templates for shotgun areas that are based on the ballistics
of small shot (no larger than 7 1/2 shot...). Shooting on a range authorized for the adapter cartridge you'll actually be firing would be good advice.
Ditto for hunting regulations.
FWIW, I have a single-shot 9mmx19 adapter for a 12ga shotgun that I purchased a long time ago. It's rifled.
Adapters are hard to come by, more so today with US ITAR export regs. It would probably be controlled as a barrel for ITAR export purposes if it was rifled.
BTW, they also make shotgun reduction adapters - .410 in 12ga for example.