Currently there are too many options as we have to offer every permutation for 3 or 4 distinct settings. These are

• Persist query or clear it each time
• Auto focus or manual focus
• JEI synchronisation or not (one way currently)

Each one should be a separate setting and potentially also extend their functionality. A option which is currently very tedious as it will exponentially grow the number of viable options.

Further we can make more precise tooltips explaining what it actually means.

Persistence

• Clear on close (existing)
• Keep, shared across all terminals (existing)
• Keep, not shared. TBD as this is a client only functionality with many edge cases and bugs (new)
• Keep, shared per terminal type. Again, client only, but a bit easier. Also extend it to the interface terminal and similar. (new)

Focus

• Manual (existing)
• Auto focus (existing)

JEI

• No synchronisation (existing)
• One way sync AE->JEI on change (existing)
• Two-way sync AE<->JEI (new)

Additionally a button to manually copy from or to JEI might be a QoL feature for anyone not wanting automatic synchronisation, but still want a quick way to filter JEI or AE on demand without typing it again.