Your video shows exactly what i asked, but only partially
Meaning, that with Dolphin opened inside your ~/.local/share/konsole/ see if when you create the profile, the file is written there, and if disappears by itself when closing Konsole.
On my end, each time i create a new_profile i get in that folder a file called new_profile.profile and remains there after i close Konsole, then i can tweak it later too.
Edit:
Found this that seems to be exactly what your issue is 458835 – Configuration files created with the create new profile button are not saved
And guess what? I managed to reproduce the issue on a VM install. If i create a New Profile and i click Apply, is in the ~/.local/share/konsole/ but once i Click OK it vanishes by itself.
Edit2:
Managed to reproduce on another install too, but i see no errors … A hacky way to overcome this issue, is to create a fake profile, running this command:
echo '[General]' > ~/.local/share/konsole/Empty.profile && echo 'Name=Empty' >> ~/.local/share/konsole/Empty.profile
Restart Konsole and then Edit/Rename/Tweak and save that profile with your settings, and make it Default.