Someone else recently had problems on Ubuntu 22 LTS. Look at this discussion here on the Groups site:
The OP never said how or if Leo finally got to work, so I've been hoping some of the suggestions helped.
In general, I have provisioned a lot of Linux VMs with Leo, including Ubuntu 22, with success. Sometimes a shared library is missing - I mean a .so file, not a Python library. Once or twice, IIRC, I had to install Qt itself, beyond PyQt, to get all the necessary parts. But I don't remember all the details or even which Linux distro was involved.
In your case, beyond suggestions on the other thread, I'd probably try to use the package manager to install Qt (it may already be present because some other program uses it, but maybe not). Some desktop managers themselves use Qt, some do not. You can probably find out about Ubuntu's with some internet searching.
On my own Ubuntu 22.04 VM (which Leo works on), a search for directories starting with "Qt" gave this:
tom@tom-ubuntu-VirtualBox:~$ find / -type d -name Qt 2>/dev/null
/usr/lib/python3/dist-packages/orca/scripts/toolkits/Qt
/home/tom/.local/lib/python3.10/site-packages/PyQt5/Qt5/qml/Qt
/home/tom/.local/lib/python3.8/site-packages/PyQt5/Qt
/home/tom/.local/lib/python3.8/site-packages/PyQt5/Qt/qml/Qt
/home/tom/.local/lib/python3.8/site-packages/PyQt5/Qt5/qml/Qt
Don't forget the 2>/dev/null or the output will be dominated by zillions of "permission denied" messages!