I have found how to reproduce the bug! PLEASE, REPAIR IT.
1) file ~/.local/share/applications/org.kde.kate.desktop contains blocks
in the following order and everything works as it should (Kate is
searchable in the dash and can be pinned to the dash bar):
[Desktop Entry]
...
[Desktop Action
So it seems that the org.kde.kate.desktop file was wrong, the [Desktop
Entry] block was generated at the end of the file instead at the top.
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** Attachment added: "the desktop file taken from Ubuntu 16.04 where it worked"
https://bugs.launchpad.net/ubuntu/+source/kate/+bug/1884432/+attachment/5385861/+files/org.kde.kate.desktop
** Description changed:
There are several issues with 'Kate' on my clean install of Ubuntu 20.04
Public bug reported:
There are several issues with 'Kate' on my clean install of Ubuntu 20.04
When I installed Kate from Snap, it could not recognize my sessions
(which I copied from my old disk to ~/.local/share/kate/sessions and I
also moved the .desktop file to ~/.local/share/applications)
** Attachment added: "No option to add to favorites or to open a new window"
https://bugs.launchpad.net/ubuntu/+source/kate/+bug/1884432/+attachment/5385859/+files/Sn%C3%ADmek%20z%202020-06-21%2015-13-16.png
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