fix(skills): speed up picker reopening and remote discovery #6119

Job	Run time
Shell Deploy Scripts	9s
Build Impact	17s
Frontend Build	9m 27s
CLI Tests (windows-latest)	14m 28s
CLI Tests (macos-15)	9m 13s
Rust Build Check (ubuntu-latest)	13m 9s
Rust Build Check (windows-latest)	36m 40s
CLI Tests (ubuntu-latest)	8m 58s
Rust Build Check (macos-15)	17m 53s
Impact-selected Linux / Relay Contract	0s
DSH Profile Packaging (windows-latest)	0s
Rust / CLI Validation	8s
	1h 50m 22s

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