## Description
Adds analytics event to log search input.
* Adds debounce to search as well.
#### PR fixes following issue(s)
Fixes#27449
#### Type of change
- Chore (housekeeping or task changes that don't impact user perception)
## Testing
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#### How Has This Been Tested?
> Please describe the tests that you ran to verify your changes. Also
list any relevant details for your test configuration.
> Delete anything that is not relevant
- [x] Manual
- [ ] JUnit
- [ ] Jest
- [ ] Cypress
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#### Test Plan
> Add Testsmith test cases links that relate to this PR
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>
#### Issues raised during DP testing
> Link issues raised during DP testing for better visiblity and tracking
(copy link from comments dropped on this PR)
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## Checklist:
#### Dev activity
- [ ] My code follows the style guidelines of this project
- [ ] I have performed a self-review of my own code
- [ ] I have commented my code, particularly in hard-to-understand areas
- [ ] I have made corresponding changes to the documentation
- [ ] My changes generate no new warnings
- [ ] I have added tests that prove my fix is effective or that my
feature works
- [ ] New and existing unit tests pass locally with my changes
- [ ] PR is being merged under a feature flag
#### QA activity:
- [ ] [Speedbreak
features](https://github.com/appsmithorg/TestSmith/wiki/Guidelines-for-test-plans#speedbreakers-)
have been covered
- [ ] Test plan covers all impacted features and [areas of
interest](https://github.com/appsmithorg/TestSmith/wiki/Guidelines-for-test-plans#areas-of-interest-)
- [ ] Test plan has been peer reviewed by project stakeholders and other
QA members
- [ ] Manually tested functionality on DP
- [ ] We had an implementation alignment call with stakeholders post QA
Round 2
- [ ] Cypress test cases have been added and approved by SDET/manual QA
- [ ] Added `Test Plan Approved` label after Cypress tests were reviewed
- [ ] Added `Test Plan Approved` label after JUnit tests were reviewed
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