Context menu cut and paste does not change findbar state

[cndouglas]

Did you search for similar issues before submitting this one?
Yes.

Describe the issue you encountered:
If you cut and/or paste with the findbar's context menu, the state does not change (i.e., the highlighted terms and number of matches do not change).

Expected behavior:
The findbar state should change whenever the findbar input changes.

• Platform (Win7, 8, 10? macOS? Linux distro?):
  All (found on macOS 10.12.x)

• Brave Version:
  0.12.9

• Steps to reproduce:

  1. Open a new Brave tab and navigate to any site.
  2. Open the findbar (Find in Page: Ctrl/Cmd+F).
  3. Copy some text from anywhere.
  4. Right-click the findbar input.
  5. Select Paste.
  6. Notice that the findbar state doesn't change.

• Screenshot if needed:
  None.

• Any related issues:
  None.

[cndouglas]

See PR #5786.

[luixxiul]

Test plan: #5786 (comment)