Enable Omnibar changes for AI Chat

[Bunn]

Task/Issue URL: https://app.asana.com/0/0/1209365332925451/f

Description:
Enable omnibar changes and add new pixels

Steps to test this PR:

1. Most of this was already tested here but a good smoke test would be good with the items bellow:
2. Focus on the fact that you don’t need to be an internal user for the Omnibar + toolbar changes to take effect
3. Check if the new pixels are being fired correctly
4. Disable Duck.ai in the address bar, go the SERP, search something, then open the address bar and start typing, check if the right side margin is good. [See bug report]

Definition of Done (Internal Only):

• Does this PR satisfy our Definition of Done?

[brindy]

LGTM