Simplify logic of how search-input layout figures out if a search page is multilingual or not.

[SayakMukhopadhyay]

This issue is being raised to track this review #49724 (comment)

You seem to be doing here manually here what GetPage can do automatically. For details, see https://gohugo.io/methods/site/getpage/#multilingual-projects

[SayakMukhopadhyay]

/assign

[sftim]

/area web-development
/area localization
/triage accepted
/priority backlog