fix(search): carry search query over to Ask Kestra AI prompt (#5354)

[iitzIrFan]

fixes: #5354

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When a search comes up empty, clicking Ask Kestra AI opened the AI dialog with a blank prompt, so you had to retype the query you just entered.

Now the text in the search box is carried over and pre-filled in the AI prompt (with the textarea focused and resized), so a failed search hands off straight to the AI.

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Ref. video:

2026-08-28.14-03-53.mov

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[github-actions]

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🔦 Lighthouse Benchmark

Tested: http://localhost:8787 on 2026-09-02 11:01 UTC
Compared against main baseline from 2026-09-02

Scores (0–100, higher is better)

Page	Performance	Accessibility	Best Practices	SEO
Home	64	84	54 🔻 -19	92
Get Started	64	83	54 🔻 -19	100
Pricing	98	92	54 🔻 -19	100
Enterprise	97	83	54 🔻 -19	100
Cloud	90	80	54 🔻 -19	100
About Us	98	91	54 🔻 -19	100
Docs Landing	95	88	54 🔻 -19	92
Contribute to Kestra (simple docs)	98	88	54 🔻 -19	92
Flow (full featured docs)	97	90	54 🔻 -19	92
Blog Index	65	91	54 🔻 -19	100
Blog Post (sample)	88 🔻 -10	88	54 🔻 -19	100
VS Page (sample)	97	88	54 🔻 -19	100
Plugins Landing	92	81	54 🔻 -19	92
Plugin Page (sample)	94	88	54 🔻 -19	100
Plugin Debug Page (sample)	92	88	54 🔻 -19	100
Plugin Debug Return Page (sample)	95	88	58 🔻 -19	100
Blueprints Landing	77	91	54 🔻 -19	100
Blueprint Audit Logs CSV Export	0	0	0	0

Core Web Vitals (lower is better)

Page	LCP	FCP	TBT	CLS	Speed Index
Home	1.25 s	0.78 s	874 ms 🟢	0.000	2.18 s
Get Started	2.02 s	0.62 s	751 ms	0.034	0.87 s
Pricing	1.03 s	0.58 s	28 ms 🟢	0.000	0.83 s
Enterprise	1.29 s	0.59 s	44 ms	0.000 🟢	0.88 s
Cloud	1.98 s	0.61 s	28 ms 🟢	0.001	0.92 s
About Us	1.04 s	0.64 s	24 ms	0.000	0.88 s
Docs Landing	1.24 s 🔻	0.57 s	119 ms	0.000	0.97 s
Contribute to Kestra (simple docs)	1.11 s	0.55 s	59 ms	0.000	0.85 s
Flow (full featured docs)	0.88 s	0.60 s	131 ms 🔻	0.000	1.08 s
Blog Index	15.76 s	0.59 s	40 ms 🔻	0.001	18.97 s
Blog Post (sample)	2.25 s 🔻	0.53 s	28 ms 🟢	0.000	0.76 s
VS Page (sample)	1.15 s	0.61 s	51 ms 🔻	0.064	0.80 s
Plugins Landing	1.10 s	0.57 s	63 ms	0.000	2.61 s
Plugin Page (sample)	1.01 s	0.60 s	55 ms 🔻	0.000	2.10 s
Plugin Debug Page (sample)	0.90 s	0.58 s	158 ms 🔻	0.000	1.92 s
Plugin Debug Return Page (sample)	0.93 s	0.62 s	63 ms 🟢	0.000	2.03 s
Blueprints Landing	2.45 s	0.99 s	40 ms	0.000	3.48 s
Blueprint Audit Logs CSV Export	0.00 s	0.00 s	0 ms	0.000	0.00 s

Legend

🟢 improved  ·  🔻 regressed  ·  (blank) no significant change
Score threshold: ±10 pts  ·  Metric threshold: ±30% of baseline

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