Moved responsibility of focusing in Duo Chat's input field down to the Duo Chat itself

What does this MR do and why?

The MR removes the external calls to Duo Chat focus on the input and delegates that responsibility to the Agentic and Classic Duo Chat components directly. The focusing in those happens automatically when an external consumer triggers the mode (a tab) in the Duo Chat.

References

How to set up and validate locally

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Related to #582543 (closed)