Thanks for the info @rokejulianlockhart
I did some testing myself and can confirm with Firefox and Chrome natively.
Didn’t work at all with Ubuntu’s Chromium Snap, i.e. the menu does not even come up.
Which leads me to an educated guess that this might be functionality provided by the Plasma Browser Integration plugin/extension.
I think that either its browser side or host side (or library called by the host side) messes this up.
KDE bugzilla “product” is plasma-browser-integration