Improve how submissions are filtered in new submission lists

[NateWr]

Describe the problem you would like to solve
The existing submission lists use a left sidebar to add or remove filters. However, the new dashboard (#8880) already has a left sidebar. Also, editors want a clearer indication of which filters are currently applied.

Describe the solution you'd like
The mockups below show a filter UI that opens a side panel to select filters, then displays the applied filters above the list. It also suggests an approach to show saved filters.

Who is asking for this feature?
This UI is necessary to adjust to changes in #8880. It has been tested with users and received positive feedback.

Additional information
The side panel is a UI pattern shared with the submissions summary view (see #8883).

The side panel with a form to add filters:

NOTE: There should also be a "Date Submitted" filter, which applies to the submissions.date_submitted column in the same way that "Days since last activity" applies to (probably) date_last_activity.

Show the applied filters above the list:

There are some more edge cases on how the different applied filters are shown:

Edge Case 1:

Edge Case 2:

Edge Case 3:

Edge Case 4: