Integrations page: Remove invisible right margin of search bar to remove scroolbar

[emufan]

Breaking change

Proposed change

Remove the not visible/additional right-margin 8px to hide/remove the scrollbar on desktop chrome, etc.

Has been introduces in mwc migration here #11637

Type of change

• Dependency upgrade
• Bugfix (non-breaking change which fixes an issue)
• New feature (thank you!)
• Breaking change (fix/feature causing existing functionality to break)
• Code quality improvements to existing code or addition of tests

Example configuration

n/a

Additional information

• This PR is related to issue or discussion: beta channel, but not beta related:
  https://discord.com/channels/330944238910963714/427516175237382144/992042475126530120

Checklist

• The code change is tested and works locally.
• There is no commented out code in this PR.
• Tests have been added to verify that the new code works.

If user exposed functionality or configuration variables are added/changed:

• Documentation added/updated for www.home-assistant.io

[zsarnett]

Thanks!