Prevent focusing in chat on page load

Denys Mishunovrequested to merge
575660-focus-in-chat-on-user-action into master

Related to #575660

The MR fixes the regression, introduced in Moved responsibility of focusing in Duo Chat's ... (!214692 - merged), where Duo Chat was constantly stealing focus from other elements. The MR ensures that Duo Chat's input gets focus only when user switches to either new, or active mode of the Duo Chat. Those actions don't happen automatically and are always initiated by the user.

Before After
CleanShot_2025-12-09_at_11.04.33__1_ focus-fixed
Edited by Denys Mishunov

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