How can I show hidden files on 'choose a file' dialog in 3rd-party apps?

As noted, you have found how to show invisibles, in Finder and in file-picker dialogs…

You are going to be hampered, however, by the fact that Spotlight will not index hidden or System locations, so they will not show up in search.

A potential partial workaround would be to open your destination folder in Finder before you need it in an app. Then, when you are presented with any file-picker dialog, you can drag that folder into the dialog & the file-picker will go to that location.