Hey there!
The part shown here is a pivot shoe. Yours instantly reminded me of the 15-177. Have a look and see if the specifications match what you need.
The 15-177 pivot shoe is compatible with a large number of different pivot bars. Overall length also doesn't really matter. What's more important is hole placement relative to the front tip (the end that goes into the pivot shoe, to be clear).
For example, one common pairing with the 15-177 is the 26-352 pivot bar. Its hole centers are set back 1-5/16" and 1-3/4" from the end. The overall length of 2-7/16" is irrelevant.
This is only one possibility, though. There are dozens of other options. I'd be happy to look into it for you, but I need a photo of the old pivot bar removed from the window and I will need to know its hole center positions, as described above.
