Allow exporting all parameters to a .param file

We already have all the parameters. All we have to do is generate a file from the parameters widget.

Bonus points: Generate a file with only the ones currently showing (with the search filter applied)

Start at the parameters widget and trace how it exposes the loaded parameters. Determine the project’s expected .param format, then verify that exporting includes all parameters and, if implemented, only the entries visible after applying the search filter.

Written by the indexing model from the issue text.