Disclaimer: I'm not sure about the procedure. Anything below this line without warranty. Don't hold me responsible for any further damage.
The folder 00000082 is missing from SYSNAND CTRNAND/data/[consoleid]/sysdata
00000082 is -- as far as I know -- the Japanese Home Menu save data on SD, not on CTRNAND.
In case of
accidental deletion the most important thing is to not write on the drive/disk/partition anymore. Data recovery or forensic software can then try to recover missing files+folders. Any write access reduces chances. Invasive and potentially destructive methods like CTRTransfer are not the first, but the last thing to try (if anything else failed).
Reinstalled HomeMenu EUR CIA via GodMode9
Mhmm.

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Step 0 -- Highly recommended
Backup the NAND now. Backup the SD as well.
Yes, the broken state. Store your data on multiple media.
After that you can try to fix the damage.
Idea A) -- Recovery Attempt
Dump decrypted CTRNAND image and try some data recovery software on PC on it. I've no knowledge about data recovery software. Maybe the missing files can be restored and the image flashed back (manually).
This is not without risks and I won't describe that in detail.
Since GodMode9 considers the
data folder Lv1 only it doesn't seem to be vital for the console itself. After all it is just user data. Assuming you didn't delete anything outside the user data folder brings us to:
Idea B) -- Factory Reset
On my test console this worked: I renamed the whole folder data on CTRNAND to data_. After rebooting the console went into initial setup like expected. This shouldn't change encryption key. Tickets might be missing.
Caveats
You already -- potentially -- changed software by reinstalling a CIA. No idea if the firmware is in a working state right now. You might have to go the radical route with CTRTransfer at the end.
Good luck!