feat: retain state between tab switches and generate suggestions from nudge flow CLOUDP-323832

[rubydong]

Description

https://jira.mongodb.org/browse/CLOUDP-323832

Previously input query would get wiped once user clicks away to the "Start with an index" flow. Also, we want to generate the suggestions when user visits from the nudge in documents tab

Screen.Recording.2025-06-11.at.12.12.39.PM.mov

Checklist

• New tests and/or benchmarks are included
• Documentation is changed or added
• If this change updates the UI, screenshots/videos are added and a design review is requested
• I have signed the MongoDB Contributor License Agreement (https://www.mongodb.com/legal/contributor-agreement)

Motivation and Context

• Bugfix
• New feature
• Dependency update
• Misc

Types of changes

• Backport Needed
• Patch (non-breaking change which fixes an issue)
• Minor (non-breaking change which adds functionality)
• Major (fix or feature that would cause existing functionality to change)