I think this started with Monterey, because on Big Sur and earlier, it always initialized in the center.
Correct me if I'm wrong, but I believe NeXTSTEP also initialized the cursor close to the top-left corner. So this might either be an homage to NeXTSTEP (similar to how the Clarus dogcow has reappeared in macOS Ventura), or a bug. My bet is on the latter.
I have to admit "where the mouse cursor is at startup" is a very minor niggle for myself, as I rarely restart / shut down computers and the password field for the last user is usually selected and will take typing by default anyway (or after Ctrl-Alt-Del on Windows, if you're old school and turn that on). After sleep modes it could be anywhere, so you're going to be reorientating yourself anyway...
Couldn't you have just logged out?
I preferred the thorough 20s restart approach.