This combination set has seen quite some modification.
The original rifle caliber is anyone's guess, may have been around 5 mm (.22 WMR/ 5.6x35R Vierling as mentioned, or 5,2x34R Kronprinz, or some 6,5mm Tesching cartridge, or something even larger).
The outside contour of the rifle barrel may give an indication.
Now I have no experience in hunting capercaillie, only stories from Dad and Granddad. In Austria and Germany Capercaillie cocks were hunted only during mating season, the bird normally sitting in a tree. If possible the shotgun barrel was used, and I am in doubt about using a 24 gauge; not much payload for a large bird.
The original purpose of the gun may have been for "Schonzeit" (quiet season) or for a lady?
When the .222 rem. insert barrel was installed in the 1960s, that Capercaillie plate was probably added to the pistol grip as an adornment, the Schwenkmontage and the rubber recoil pad come from the same time, or even later.
The 24 ga shotgun barrel set may have been with a Wiener Schnäppermontage, funny thing for a shotgun at that time.
fuhrmann