Local Firefox Profiler as single static binary
The “official” firefox profiler is hosted at https://profiler.firefox.com/. Firefox itself does not provide its own local-only profiler anymore, but any profiles you create (or upload) will be opened on the Mozilla-hosted website.
Mozilla employees assured me that currently no telemetry is used on profiler.firefox.com, but the linked privacy policy basically allows Mozilla to do any kind of data collection (breaching GDPR …).
However, it is possible to change the profiler Firefox uses to an arbitrary URL.
In about:config, set the preference
devtools.performance.recording.ui-base-url
to http://localhost:5252 (or whichever port you use):

So if you want to host your profiler yourself (e.g. on your local machine or in your own company network (profiles are IP-critical pieces of data!), you can use this nix expression to build a simple golang binary which serves the javascript files.
nix run https://sources.profpatsch.de/Profpatsch.tar.gz#firefox-profiler