refactor: Updates the reduced nav search to use newest Vanilla pattern

[petesfrench]

Don't merge: Until the branch this PR references has been merged

Done

• Updates the reduced navigation to use the latest vanilla pattern, found here https://github.com/canonical/vanilla-framework/pull/5210
• It moves the search to be all in the 'normal' navigation

QA

• Open demo
• Check the search functionality, both on desktop and mobile screen sizes

Issue / Card

Fixes https://warthogs.atlassian.net/browse/WD-13043

[webteam-app]

Demo

Jenkins

demos.haus

[akbarkz]

Two finding during QA:

1. The word "Canonical" is not aligned with the bubble logo below

2. When clicking on "Menu" button on mobile screen, it navigates to /navigation. It wasn't like this before.

[petesfrench]

@akbarkz

1. I flagged that with Bartek and he informed me that is the expected behaviour, see the conversation
2. That is the fallback link for when JS fails/doesn't load etc. In this case, as this is the sliding nav, the JS doesn't exist. So this is the expected behavior