I don't see a way to file an issue ticket on Github, so I hope this will do.
I've run up against an issue that may have to do with changes Apple made to the location (or absence) of OpenGL frameworks on macOS 11 (Big Sur).
Calibre 5.5 was fine until I activated its web server. Now launch does not complete. The splash screen appears, then the app stops trying to load.
I then launched it from the terminal with the debug option to see what I could learn. The final line in the terminal before stopping is "FileNotFoundError: [Errno 2] No such file or directory." I am attaching that terminal session here.
In the system logs, there are these three Calibre-related lines at the same time:
Nov 23 13:54:19 My-Server-Name com.apple.xpc.launchd[1]: Coalition Cache Hit: app<application.net.kovidgoyal.calibre.12930261220 .12930261347(501)> [856]
Nov 23 13:54:26 My-Server-Name calibre[816]: getattrlist failed for /System/Library/Extensions/AppleIntelHD5000GraphicsGLDriver.bundle/Contents/MacOS/AppleIntelHD5000GraphicsGLDriver: #2: No such file or directory
Nov 23 13:54:26 My-Server-Name calibre[816]: getattrlist failed for /System/Library/Frameworks/OpenGL.framework/Resources//GLRendererFloat.bundle/GLRendererFloat: #2: No such file or directory
A quick Google search for relevant terms turns up many other projects running up against this problem. This discussion here seems relevant and enlightening:
https://github.com/ziglang/zig/issues/2208
I hope this is helpful. Thanks for the project and all the hard work over the years.