Fix showing two modals after pressing ctrl+k or / to open the search modal for the first time

[DamianMaslanka5]

Current behavior is very annoying, so I decided to just fix this.

closes #3191, closes #3271

mp4 from #3191 (comment) (this a bit old, now there are only two modals instead of three)

msedge_0W46PhmL8K.mp4

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[DamianMaslanka5]

DocCheck failed because of the issue fixed in ClickHouse/ClickHouse#81469, so I guess that re-running the job will fix it

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[Blargian]

@DamianMaslanka5 this fixes the docs search but breaks the mobile menu at certain widths bigger than the docusaurus breakpoint. See below (hamburger is missing):

The current mobile menu system is terrible, I'll merge something shortly to fix and then we can integrate this change.

[DamianMaslanka5]

@Blargian nice catch, I was thinking only about desktop and mobile breakpoints.

There are two solution for this issue:

1. Make sure only one SearchBar is loaded
2. Change SearchBar to make sure only one modal can be opened

Let's wait for #3890, then let's get back to this and see which solution makes sense.

[DamianMaslanka5]

@Blargian I decided to go with 2. from #3909 (comment). I rebased the branch and force pushed the changes.

Changing the SearchBar component is better because now we can be sure that another change to the layout will not reintroduce the issue.

[Blargian]

LGTM!