Update findbar state onInput

[cndouglas]

• Submitted a ticket for my issue if one did not already exist.
• Used Github auto-closing keywords in the commit message.
• Added/updated tests for this change (for new code or code which already has tests).
• Ran git rebase -i to squash commits (if needed).

Fixes #5753

Test Plan:

• Open a new Brave tab and navigate to any site.
• Open the findbar (Find in Page: Ctrl/Cmd+F).
• Copy some text from anywhere.
• Right-click the findbar input.
• Select Paste.
• Make sure the highlighted matches and number of matches change accordingly.

[luixxiul]

Was this reviewed?

[bsclifton]

@luixxiul not yet- did you want to check it out and give it a try? 😄

[cezaraugusto]

elegant solution, thanks!