feat: now StarSearch uses the new StarSearch API endpoints for chat creation/updates

[nickytonline]

Description

Now StarSearch chat creation and subsequents question during the same sessions are persisted to a thread. This work is a precursor to #3527 and part of the work in #3551.

Note: Prompt sharing will not work in beta for a short period of time. I will be getting this sorted out in the rest of the work for #3551 in #3563.

Related Tickets & Documents

Relates to #3551 Relates to #3563

Mobile & Desktop Screenshots/Recordings

Steps to QA

1. Start a StarSearch conversation via a canned suggestion or your own prompt.
2. Things behave like they did before including loading widgets if you ask about the lotto factor.

Tier (staff will fill in)

• [ ] Tier 1
• [ ] Tier 2
• [x] Tier 3
• [ ] Tier 4

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