Fix TemplateResponse deprecation warning in Starlette

[Copilot]

Starlette changed the TemplateResponse signature to require Request as the first parameter instead of the template name.

Changes:

• Updated api/routes/auth.py home route to use new signature: TemplateResponse(request, name, context) instead of TemplateResponse(name, {"request": request, ...context})
• Removed request from context dict as it's now automatically injected

# Before
return templates.TemplateResponse(
    "chat.j2",
    {"request": request, "is_authenticated": is_authenticated_flag, ...}
)

# After
return templates.TemplateResponse(
    request,
    "chat.j2",
    {"is_authenticated": is_authenticated_flag, ...}
)

Original prompt

---

This section details on the original issue you should resolve

<issue_title>templating.py:162: DeprecationWarning</issue_title>
<issue_description>```
/usr/local/lib/python3.12/site-packages/starlette/templating.py:162: DeprecationWarning: The name is not the first parameter anymore. The first parameter should be the `Request` instance.
Replace `TemplateResponse(name, {"request": request})` by `TemplateResponse(request, name)`.

## Comments on the Issue (you are @copilot in this section)

<comments>
</comments>

• Fixes templating.py:162: DeprecationWarning #315

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