the years from 1888 to 1898 were called the "carbinetime" in Suhl

if Schilling got the actions from Haenel there was not so much left over for them to do because I think we agree that the action is the most important part when building a gun.
I see no reason why Schilling had engraved the actions then with the own name on this part when it came from haenel.
that was not common.

your carbine was made in 1906 when no carbine 88 were ever made anymore for german authorithies

the text to number 7781 stated "suchlike in use with the german cavalry"

why "suchlike" and not "original military carbines"? at least your carbine was produced in a time when production changed for the carbine 98 completly but Suhl was still making the carbine 88.

here a Haenel 1907 made carbine in 7x57 for south america

of course there was a use of not accepted parts or guns that were sold on the civilian market.