All entries in the "New" context menu have disappeared

Note as I said before, if the problem is specific to this user account alone, this is unlikely to help.


There's a full tutorial. Try searching the tutorial section for "in-place".

And I've posted the short instructions (4 lines) many times. E.g.
Download a Win 10 iso file- same build as you have now. (Tutorial available).
Rt click the iso file, click Mount (if available)
Open the new drive letter created in file explorer
Double click setup.exe


Ghot posted a posher version here e.g.
Update from 19041.985 impossible, keeps rolling back

That's why I always put this in bold:

an in-place upgrade repair install which keeps all progs and data

Note as you say you have build 19043... this will take you to 19044, assuming you are using e.g. the MS media creation tool to get the iso file.

Check out this post:
Broken "New" context menu entry from right click on desktop - Page 2 - Windows 10 Support

Thanks- Shellexview (free) is certainly worth a go - temporarily disabling all non-MS shell extensions.
ShellExView - Shell Extension Manager For Windows

(Note, however, this problem applies to both this and a new account, and that WinAssociated has no clue about anything changing when this happened - but that doesn't necessarily exclude the effect of installing some program).

There is no real next. Diagnosing upgrade failures is complicated, tedious, iterative and requires detailed analysis of specific log files. Only a couple of people here have both the expertise and have been willing to give the time over days to help people for free, and I haven't seen any such threads for quite a long time.

You can research SECOND_BOOT during the operation BOOT and the code 0xC1900101 - 0x40017 - which is somewhat similar to the one related to driver issues, but here at a different stage, so could be something different.

Your starting point would be to validate the integrity of the existing O/S, and remove any security software and extraneous hardware. Then you can look and see how such diagnosis has been done e.g. find threads mentioning

setupdiag.exe

as an example.

It's not clear how you attempted the in-place upgrade repair.

Here are basic 'safe' steps:
a. Create a disk image of what you have now- just in case something goes badly wrong.
b. Check your disk(s) (e.g. Hard Disk Sentinel)
c. If ok, run
chkdsk c: /scan
from an admin command prompt
d. If ok, run
SFC /SCANNOW
similarly
Proceed if ok.
Uninstall any less common 3rd party security programs.

Check you have at least 30Gb free on C:

1. download the iso file (e.g. using the MS media creation tool if your build is 19044)
Tutorial available - includes how to get older builds.
2. right click the iso file
3. click Mount (available by default)
4. disconnect the internet (you're NOT going to get updates as part of this right now)
5. Open new drive letter created
6. Double click setup.exe

Now consider your error number. See e.g.
FIX 0xC1900101 - 0x40017: Installation failed in SECOND_BOOT phase in Windows 10 Update. (Solved) • Repair Windows™

Note: no guarantees of an easy solution here.