This file is not executable, or a script. Delete this line.
The Categories/direcory is not valid, or not used properly.
For a test, add this line in the Desktop Entry section of the vivaldi-ljglmmfoegmmiblmgnnkgmlnmhhojdmm-Default.desktop file:
Categories=Documentation;Network;
I assume the file is in ~/.local/share/applications . If not, copy/move it there.
Then, run this command and post output:
update-desktop-database -v ~/.local/share/applicationsupdate-desktop-database -v ~/.local/share/applications
Search path is now: [/home/ajgringo619/.local/share/applications]
File "/home/ajgringo619/.local/share/applications/vivaldi-bbcjjjnjadiebjnoekjghhbjddadjgfc-Default.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/vivaldi-nifhnpbdbefleghnfomoiakbgpkddjad-Default.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/vivaldi-odnndenhaigmjemdocmpmpfjjihanaen-Default.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/qt6-assistant.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/qt6-designer.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/qt6-linguist.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/qt6-qdbusviewer.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/vivaldi-ojibjkjikcpjonjjngfkegflhmffeemk-Default.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/vivaldi-jnpecgipniidlgicjocehkhajgdnjekh-Default.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/vivaldi-effhbfeajdkmnbdcilniclmddhibcoli-Default.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/vivaldi-nmnilcjipdidhpllfilddbnmanplhbjh-Default.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/vivaldi-epkcefmpkcdjhchbkceoenebanfnlofp-Default.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/vivaldi-dghdnjdlennabpboncgekebgdlcgiopj-Default.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/org.moson.pacseek.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/unison.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/bssh.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/bvnc.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/avahi-discover.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/lstopo.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/jconsole-java-openjdk.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/jshell-java-openjdk.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/scrcpy.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/scrcpy-console.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/stoken-gui.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/stoken-gui-small.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/GoMule.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/ph-u.desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/My Phone (TCP-IP).desktop" lacks MimeType key
File "/home/ajgringo619/.local/share/applications/Spotify.desktop" lacks MimeType key
No entries were added.
How do you search? 
I suppose you have added all the rest of the files yourself.
Was there a reason?
Are they all in the menu? If so, post contents of one file (shown in menu) that you are sure it is one of them (not the default from system).
I’ve already done that. All of the other web apps listed were added when I was running Xfce and Cinnamon. When I reinstalled with KDE, these apps were in the new menu as expected. All of the vivaldi-* .desktop files are web apps, with only the one created after I installed KDE.
Post contents of one or two of them, please.
It seems very weird to have this behavior for only one file, without any real reason to be invalid.
This has happened with multiple attempts with web apps, not just this one file.
Here’s the latest one that does not work:
vivaldi-pjibgclleladliembfgfagdaldikeohf-Default.desktop
[Desktop Entry]
Comment=
Exec=/opt/vivaldi/vivaldi --profile-directory=Default --app-id=pjibgclleladliembfgfagdaldikeohf
GenericName=Music, podcasts
Icon=Spotify
MimeType=
Name=Spotify
StartupNotify=true
StartupWMClass=crx_pjibgclleladliembfgfagdaldikeohf
Terminal=false
TerminalOptions=
Type=Application
Version=1.0
X-KDE-SubstituteUID=false
X-KDE-Username=
NoDisplay=false
Hidden=false
And one that does:
vivaldi-jnpecgipniidlgicjocehkhajgdnjekh-Default.desktop
[Desktop Entry]
Comment=Secure email
Exec=/opt/vivaldi/vivaldi --profile-directory=Default --app-id=jnpecgipniidlgicjocehkhajgdnjekh
Hidden=false
Icon=/home/ajgringo619/Pictures/websites-icons/proton-mail.ico
Name=Proton Mail
NoDisplay=false
Path=
StartupNotify=true
StartupWMClass=crx_jnpecgipniidlgicjocehkhajgdnjekh
Terminal=false
TerminalOptions=
Type=Application
Version=1.0
X-KDE-SubstituteUID=false
X-KDE-Username=
It doesn’t make sense 
.
Add a keyword in a failing desktop entry and search this from Plasma menu.
Keywords=endeavour;forum;
Update DB after editing, as previously done.
At this point, I’m at a loss. It’s got to be related to installing with some of the old Xfce/Cinnamon conifs left over. I just tried installing a web app on a clean Arch KDE VM and it worked perfectly.
I think my best bet is to start completely clean. I really appreciate all the help/suggestions.
UPDATE: clean install, apps are finally installing properly. I wish I knew what exactly happened, but at least it’s working now.