fix(headless/ssr-commerce): standalone search box only for listing & standalone

[alexprudhomme]

https://coveord.atlassian.net/browse/KIT-3762

I found out what the problem was last time I tried this when I was reading jp documentation PR 😆. We were using searchEngineDefinition in the cart and in the product page instead of standaloneEngineDefinition. This works well !

[github-actions]

Pull Request Report

PR Title

❌ Title should follow the conventional commit spec:
<type>(optional scope): <description>

Example: feat(headless): add result-list controller

Live demo links

• Storybook

• Playwright report

Bundle Size

File	Old (kb)	New (kb)	Change (%)
case-assist	242.6	242.6	0
commerce	347.3	347.3	0
search	413.8	413.8	0
insight	404.9	404.9	0
recommendation	254.9	254.9	0
ssr	407.3	407.3	0
ssr-commerce	362.3	362.3	0

SSR Progress

Use case	SSR (#)	CSR (#)	Progress (%)
search	39	44	89
recommendation	0	4	0
case-assist	0	6	0
insight	0	27	0
commerce	0	15	0

Detailed logs

search : buildInteractiveResult
search : buildInteractiveInstantResult
search : buildInteractiveRecentResult
search : buildInteractiveCitation
search : buildGeneratedAnswer
recommendation : missing SSR support
case-assist : missing SSR support
insight : missing SSR support
commerce : missing SSR support