[Docs] Version dropdown side-by-side with search box

[asfimport]

Small follow-up on #11283 to improve the styling of the version dropdown.

Reporter: Krisztian Szucs / @kszucs
Assignee: Joris Van den Bossche / @jorisvandenbossche

PRs and other links:

• GitHub Pull Request #11563

_{Note: This issue was originally created as ARROW-14499. Please see the migration documentation for further details.}

[asfimport]

Krisztian Szucs / @kszucs:
Issue resolved by pull request 11563
#11563