LTTng

https://github.com/lttng/lttng-ust/tree/v2.13.5#building-steps

reads

LTTng-UST needs to be a shared library, even if the tracepoint probe provider is statically linked into the application.

is it "impossible" to produce a static variant (liblttng-ust.a) which the user can link with their my_code_with_provider_probe_and_main_entrypoint.o and -static flag to get a statically linked executable?

in case it is technically possible but deemed uninteresting scenario by devs, please know that most libraries in distro packages provide static lib option (openssl and icu are two big names but list goes on and on) and there are use-cases which require this kind of isolation.