Do you have Edge Chromoim properly installed & working? What version is it?
Scan your full hard disk for possible old versions of the webview*.dll files and delete the old versions.
Remember, the ones you sent me with the ZIP I put in windows\systems32 and removed all others. All others you see now seem to have been installed by the FNC components and they are even newer than the ones you sent me with the ZIP.
Ok, uninstalled the trial TMS FNC components and this did not delete the DLLs in SysWOW64. I can confirm that the Web Designer for Web Core now works with these DLLs in SysWOW64.
Then I deleted these DLLs as well and copied the ones you sent me into SysWOW64. Can confirm Web Designer still works.
So, after all, it was just to put the DLLs into the right place, which is (in my case...) Windows\SysWOW64.. This is an information you might want to take note of.