@bschaaf installed ST over the official apt repository but my terminal was installed via snap.
I traced the problem down to how I installed my terminal emulator. I’m using the terminal emulator alacritty, installed via snap and something goes wrong in a snap environment context. I removed the snap version and installed alacritty in a other way. After that ST will start as expected. There are no snap specific lib path anymore. Now my
ldd /opt/sublime_text/sublime_text looks like yours @rwols
linux-vdso.so.1 (0x00007ffdfb95d000)
librt.so.1 => /lib/x86_64-linux-gnu/librt.so.1 (0x00007f8435802000)
libdl.so.2 => /lib/x86_64-linux-gnu/libdl.so.2 (0x00007f84357fc000)
libgobject-2.0.so.0 => /lib/x86_64-linux-gnu/libgobject-2.0.so.0 (0x00007f843579c000)
libglib-2.0.so.0 => /lib/x86_64-linux-gnu/libglib-2.0.so.0 (0x00007f8435673000)
libGL.so.1 => /lib/x86_64-linux-gnu/libGL.so.1 (0x00007f84355eb000)
libX11.so.6 => /lib/x86_64-linux-gnu/libX11.so.6 (0x00007f84354ae000)
libm.so.6 => /lib/x86_64-linux-gnu/libm.so.6 (0x00007f843535d000)
libpthread.so.0 => /lib/x86_64-linux-gnu/libpthread.so.0 (0x00007f843533a000)
libc.so.6 => /lib/x86_64-linux-gnu/libc.so.6 (0x00007f8435148000)
/lib64/ld-linux-x86-64.so.2 (0x00007f843582b000)
libffi.so.7 => /lib/x86_64-linux-gnu/libffi.so.7 (0x00007f843513c000)
libpcre.so.3 => /lib/x86_64-linux-gnu/libpcre.so.3 (0x00007f84350c9000)
libGLdispatch.so.0 => /lib/x86_64-linux-gnu/libGLdispatch.so.0 (0x00007f8435011000)
libGLX.so.0 => /lib/x86_64-linux-gnu/libGLX.so.0 (0x00007f8434fdb000)
libxcb.so.1 => /lib/x86_64-linux-gnu/libxcb.so.1 (0x00007f8434fb1000)
libXau.so.6 => /lib/x86_64-linux-gnu/libXau.so.6 (0x00007f8434fab000)
libXdmcp.so.6 => /lib/x86_64-linux-gnu/libXdmcp.so.6 (0x00007f8434fa3000)
libbsd.so.0 => /lib/x86_64-linux-gnu/libbsd.so.0 (0x00007f8434f89000)
Thanks for the fast help!