fix(core): omit undefined search metadata

[caddydove]

Fixes #37650

Only include provided optional search inputs in pending permission metadata, so the response remains JSON-encodable.

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[github-actions]

The following comment was made by an LLM, it may be inaccurate:

Based on the search results, I found two potentially related PRs:

1. PR fix(core): omit undefined optional keys from glob/grep permission metadata #37965 - fix(core): omit undefined optional keys from glob/grep permission metadata

   • fix(core): omit undefined optional keys from glob/grep permission metadata #37965
   • Appears to address a very similar issue: omitting undefined optional keys from permission metadata

2. PR fix(core): drop undefined metadata values from permission requests #37679 - fix(core): drop undefined metadata values from permission requests

   • fix(core): drop undefined metadata values from permission requests #37679
   • Also seems to handle undefined metadata values in permission requests

These PRs appear to be addressing the same underlying problem space (undefined values in permission metadata causing JSON encoding issues), though they may target different specific areas (glob/grep vs. search). You should verify whether PR #38381 duplicates or complements the fixes in these other PRs, or if they've already been merged/closed.