Ubuntu's package for apitrace is OLD. It's based on a git snapshot from 2012. Its version of qapitrace doesn't support core profile. There's no equivalent package in Debian.
This is a package of apitrace 6.1 for Ubuntu. I'm not going to pretend it's good. I'm pretty sure Debian would reject it with extreme prejudice (e.g. the removal of LICENSE.txt; that change comes from the Ubuntu package, and I don't know why they did it). It was NOT built cleanly (not even remotely). However, it does appear to work (at least on my machine).
Note that the dependencies are probably a little off; the Ubuntu package uses the system's version of Snappy and zlib. That's the way it typically goes in Debian, but I think using the bundled ones is justified in this case: it prevents symbol conflicts if the program being traced loads different versions of those libraries.
If you just want to run it, grab the two .deb files below. If you want to build it from source, grab the two .tar.xz files and the .dsc file. If you're wondering what's in them, the orig.tar.xz file should contain the same files as a git checkout of apitrace with the "6.1" tag (minus .git). debian_changes.diff lists the changes from Ubuntu's .debian.tar.xz.
No, the packages aren't signed. My development machine doesn't have my GPG key on it. I'll upload signed packages once I make some good packages.