Mouse without border: KeysNotMatched

### Microsoft PowerToys version

0.101.2362.0

### Installation method

WinGet

### Area(s) with issue?

Mouse Without Borders

### Steps to reproduce

Configure connection through MWB settings -> KeysNotMatched / Invalid Key.

I tried :
- different generated keys
- copy paste though buffer sharing (LocalSend) or manually enter the key
- using the "Setup", or changing the "Security key" to the exact same one
- using my own 16 digit (the simplest tried being: 1234567890123456)
- With IP mapping and without
- resintalling

### ✔️ Expected Behavior

Connection

### ❌ Actual Behavior

KeysNotMatched / Invalid Key

### Upload Bug Report ZIP-file

_No response_

### Additional Information

WORKAROUND: Go to "%localappdata%\Microsoft\PowerToys\MouseWithoutBorders\", edit "settings.json" and add the same MANUAL_KEY in the files with the same path on the two computers.
Attention : MWB must be closed, otherwise the value is overwritten (see Hypthesis 1 for the overwritting value).
settings.json =
{
"properties": {
"SecurityKey": {
"value": "MANUAL_KEY"
[...]

HYPOTHESIS 1 : My attempts of configuration were through the interface of MWB itself, I noticed after the manual change that there is also a configuration interface in PowerToys. The value was overwritten when editing the file without exiting MWB.
Maybe PowerToys and MWB are conflicting, writing both their value in the file, preventing a change.
HYPOTHESIS 2: Some special char are not properly escaped.

### Other Software

_No response_

Start with the Mouse Without Borders settings flow and the settings.json files under %localappdata%\Microsoft\PowerToys\MouseWithoutBorders\, comparing how SecurityKey and MANUAL_KEY are written on both computers. Reproduce the interface configuration and file-edit workaround while PowerToys is closed, then trace which value is overwritten. Done means a normal MWB setup connects without requiring manual JSON edits.

Written by the indexing model from the issue text.