Ignore what below the -=-=-=--=--=--== line. Not sure how you got into a the hunt for a phantom lib. Started from scratch by downloading the rustdesk 1.1.9.deb, extracting, checking with ldd then built a pet, supplying the newer version of xdotool it being the only missing lib reported under Bionicpup64 (I was using at the time). Started rustdesk via a terminal which reported:
INFO:TIS: scaleFactor 1
INFO:TIS: current platform: Linux
INFO:TIS: is_xfce: false
INFO:TIS: id updated
But, like you got:

- rustdesk gui.png (36.53 KiB) Viewed 2079 times
Will boot into Fossapup64 and see if there's a difference.
Booted into Fossapup, repeated the above, except that ldd didn't even suggest that a newer xdotool was needed. But got the same results, except that no update to id showed in the terminal output.
Included in the 1.1.9.deb was a control file revealing these dependencies:
Depends: libgtk-3-0, libxcb-randr0, libxdo3, libxfixes3, libxcb-shape0, libxcb-xfixes0, libasound2, libsystemd0, pulseaudio, python3-pip, curl. (Emphasis supplied). ListDD tells nothing about python, and about which I am also clueless.
My other thought is that Fossapup may not employ the same 'infra-structure' as Ubuntu Fossa Focal between X11 and applications. But I would have thought ldd would have noticed that something was missing.
-=-=-=--=--=--==
"Made symlink libssl.so.1.2.1 to libssl.so.1.1" may be the cause of the problem. libs are often backward compatible, but not 'forward' as that requires the compiler to be a prophet.
Don't know who the rust Devs had in mind for their application. Although I didn't check all distributions covered by pkgs.org, a quick scan revealed that no OS was using a libssl 'newer' than libssl.so.1.1 other than:
Fedora 35 & 36 >libssl47-3.4.2-1.x86_64.rpm; and openSUSE Tumbleweed >libssl52-3.5.3-1.3.x86_64.rpm. And while those higher numbers might just have been a difference in the naming conventions used by those distros, a quick check of libssl52-3.5.3-1.3.x86_64.rpm's dependencies revealed among them libc.so.6(GLIBC_2.36)(64bit). IIRC, Fossapup64 employs glibc-2.30, so would not be able to use that library even via a symlink named 1.2.1.