This worked for me as well, thank you so much nko123!
The Windows 11 Installation Assistant was completely useless to me; it did an installation and then my version was still 22H2.
What ultimately fixed things was this random update package that Windows Update somehow couldn't find but is needed for Windows update to "see" and attempt to install the 23H2 update.
Search for "Windows Update KB5027397". Microsoft doesn't provide it because it's supposed to be downloaded automatically; obviously it's failing to do that. I found the direct download on this page. I used the printed url version rather than the "Download" button that requires you have an account.
Once I installed that update and restarted my computer, Windows update immediately started downloading the 23H2 update. Hope this helps!