feat: sync states between layouts

[Andrewnt219]

Description

Currently, if you enter something in the search bar and go to another page, the input will be reset. This is because Next.js doesn't recognize the nested layout as the same layout, so it doesn't do proper reconciliation.

Video shows fixed version.

https://www.awesomescreenshot.com/video/6012782?key=be957f01eb589a6bab38a61015fdd93c

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🔍 Inspect: https://vercel.com/andrewnt219/rent-near-me/ARVe6YdD27GBWYeUpED1EmRfc8Hj
✅ Preview: https://rent-near-me-git-sync-layout-states-andrewnt219.vercel.app

[vitokhangnguyen]

Good discover of the isssue 👏

[vitokhangnguyen]

Change base to main as well, we're doing house keeping, we only merge to dev when we have a milestone