SUMMARY
The session chooser has no shortcuts on the buttons for “New Session”, “Open as Template”, “Duplicate”, the checkbox “Don’t ask again”, (and also for the input field for the filter, or to get to the list of sessions).
This is true for English and German.

STEPS TO REPRODUCE
1. Press [Ctrl]-[Shift]-[,] (“Settings”→“Configure Kate …”), press [Tab] four times (why not just once?) and press down [↓] five times (“Session“), [Tab] twice (“Application startup behavior”), Then press down [↓] until “Manually choose a session” is selected. Now press [Return], and close Kate.
2. Open Kate. The session chooser dialog will appear.
3. Try to just open an empty new session.

OBSERVED RESULT
There is no shortcut. One has to cumbersomely [Tab] through the entire thing. (Which suggests that the programmers aren’t exactly keyboard users. ;)

EXPECTED RESULT
There used to be shortcuts. It looks like somebody messed up, (or somebody with very little experience in using anything more than an iPad intentionally made that choice? ;)

SOFTWARE/OS VERSIONS
Linux/KDE Plasma: Gentoo Linux “2.17” (According to kinfo. No idea where it got that version from, this is the default/linux/amd64/23.0/desktop/plasma profile, updated yesterday, with no relevant overlays.)
KDE Plasma Version: 6.4.1
KDE Frameworks Version: 6.15.0
Qt Version: 6.9.1

ADDITIONAL INFORMATION
In generally, Kate, an application that literally exists for keyboard users, is shockingly hostile to keyboard users. Which is surprising, for such an otherwise so powerful editor.

May I suggest to encode a general rule in the compilation and build process that enforces that all commands are (modules or objects or) data structures that must register for any context they want to be reachable from, and to do that, must (!) have a keyboard shortcut and button (which includes menu items) available from that context, and for the build to fail otherwise?