Reflect filter selections in the search query input

Selecting a value in the filter sidebar applies it to the search, but the query input doesn't show it. Filter state and query text live in two places, so the input never reflects the full set of conditions actually being applied.

Make the two representations one: selecting a filter writes the corresponding condition into the query input, and editing the query updates the filter selections to match.

Notes:

• Needs to work for both query dialects the input supports, which is the main source of complexity — round-tripping requires parsing query text back into filter state, not just generating it.
• Today this is partially addressed by pills rendered below the input, which surface that filters are applied without making them editable as query text.

Start at the filter sidebar and query input, then trace how the existing filter state, query text, and rendered filter pills are connected. Check both supported query dialects and identify the parsing and generation entry points. Done means selecting filters updates editable query text and editing either dialect updates the corresponding filter selections without losing conditions.