But sprintf() is not a ESP32 Arduino library function. That’s in the realm of the XTensa GCC compiler / the C library it uses, aka newlib.
I consider a “Arduino library function” as something implemented in core/esp32 or in libraries/.
The Espressif GCC toolchains come from Releases · espressif/crosstool-NG · GitHub. Deep inside there are the configuration files for newlib and the header files for stdio.h, string.h, et cetera. This at least tells you if a function is supposed to exist in accordance to the header file. PlatformIO also allows you to follow a function name to its declaration (Ctrl+Click on identifier).
As far as I know, noone has ever bother to setup a documentation page for “these are exactly the functions that work in our XTensa GCC / newlib configuration”. But you can assume a lot of standard stuff works – sprintf() of course too.
If you really wanna look at the source, I linked the repo for newlib above. sprintf() is in there too, of course.
Goodness, that’s straight into my bookmarks. The documentation section is terrific. Easier to understand than the equivalent man page. What is really good is that, if you’re after a particular variant of a function whose source doesn’t include documentation, there’s a note giving the variant that does include it. Love it; no more dtostrf for this boy.