Rework landing page to be less jarring, unifi search bar components

[Yantrio]

This PR sits on top of #338

It does the following:

• Unify the search bar components, as they were all a mess!
• Make the landing page much less jarring by not altering the UI when you hit the search bar

Checklist

• I have read the contribution guide.
• I have not used an AI coding assistant to create this PR.
• My contribution is compatible with the MPL-2.0 license and I have provided a DCO sign-off on all my commits.
• I have written all code in this PR myself OR I have marked all code I have not written myself (including modified code, e.g. copied from other places and then modified) with a comment indicating where it came from.

[cloudflare-workers-and-pages]

Deploying registry-ui with    Cloudflare Pages

Latest commit:	3acb275
Status:	✅  Deploy successful!
Preview URL:	https://43d8828c.registry-ui-dxi.pages.dev
Branch Preview URL:	https://search-experience-rework.registry-ui-dxi.pages.dev

View logs

[yottta]

Feels way better. I am not sure, but feels that something is still missing. Maybe others have a more valuable feedback.

[Gogotchuri]

The old homepage was better—more clarity and a simple UX, featuring a single search bar with a good call to action.
The main issue was that the jump to a different layout occurred as soon as you started searching, which was jarring and unexpected.
One thing I can think of is leaving the Home page as it was before and changing the search bar so that it displays the autocomplete list of items. We can then jump to the resource once the user clicks or presses Enter. This is the intended action and shouldn't be an issue.
The corner search bar can be reused here.

P.S. Another thing I have overlooked - We should remove that corner search bar entirely. Having two search bars on pages is a bit confusing and unnecessary.