For Luger P08 - QED (IMHO)
Don't worry about the apparently tight measurement - I wouldn't trust my supermarket cheapo slide gauge to the last mm anyway! And it was probably supposed to be a tight fit, to stop the insert rotating when firing.
It's for a Luger P08, as I guessed at the start. They were made with barrel lengths of 100, 120, 150 and 200 (nominal) mm. It looks as if you have the version for the standard 100mm army barrel. The rifled insert is long enough to be used with the other lengths up to the 200mm for the LP08 a.k.a. artillery Luger. To achieve this, you will probably find that the slimmer section of the aliminium tube screws into the thicker section with the sight slot. The slimmer section would have been available in various lengths to suit the various barrels.
I would love to have it for my LP08, but I can tell you right now I couldn't afford it! Luger collectors love that sort of thing, and if you got it for less than a 3-figure price it was a good deal.
All this is, of course, just my enthusiastic opinion!
Now go and find a Luger owner (gun club?) and try it out!