docs: add example for updating user metadata

[Aryan31v]

This PR adds a specific code example and documentation for updating user app_metadata and user_metadata via the auth.update_user() method. This addresses common confusion regarding how to handle these dictionary-based fields in the Python client.

Summary by CodeRabbit

• Documentation
  • Added a new "Metadata Update" example showing how to update app_metadata and user_metadata (includes a Python usage snippet).
  • Reflowed documentation navigation entries to improve the examples index formatting.

[coderabbitai]

📝 Walkthrough

Walkthrough

Adds a new documentation example page demonstrating how to update app_metadata and user_metadata via auth.update_user(), and updates the examples index to include the new "Metadata Update" entry. Changes are documentation-only; no code logic modified.

Changes

Cohort / File(s)	Summary
Documentation — examples src/auth/docs/source/examples/index.rst, src/auth/docs/source/examples/metadata_update.rst	Inserted a new metadata_update.rst example showing a Python snippet that updates app_metadata and user_metadata via auth.update_user(), and adjusted the examples toctree in index.rst to include the new page.

Estimated code review effort

🎯 1 (Trivial) | ⏱️ ~2 minutes

🚥 Pre-merge checks | ✅ 3

✅ Passed checks (3 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title clearly and accurately summarizes the main change: adding a new documentation example for updating user metadata. It directly relates to the primary content of the changeset.
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.

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✨ Finishing touches

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Post copyable unit tests in a comment

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[coderabbitai]

Actionable comments posted: 3

🤖 Fix all issues with AI agents

In `@src/auth/docs/source/examples/index.rst`:
- Around line 13-15: The toctree entries have inconsistent indentation: "API
</api/api>" and "Client </api/client>" are aligned but "Metadata Update
</examples/metadata_update>" is misindented; edit the toctree so that the
"Metadata Update </examples/metadata_update>" line uses the same leading spaces
as the other entries (match spacing of "API </api/api>" and "Client
</api/client>") to ensure all entries are vertically aligned in the toctree.

In `@src/auth/docs/source/examples/metadata_update.rst`:
- Around line 34-38: The example uses auth.update_user() incorrectly: remove the
trailing .execute() call and the "id" field because auth.update_user() updates
the currently authenticated user and returns the response directly; replace the
payload to only include "app_metadata" and "user_metadata". If you intended a
server/admin update by ID, call auth.admin.update_user_by_id(user_id, {...})
instead of auth.update_user() and pass the metadata object as the second
argument.
- Around line 40-43: Remove the erroneous .execute() call after
supabase.auth.update_user and replace the response.error check with a
try/except: call supabase.auth.update_user(...) directly inside a try block,
print success on success, and catch Exception as e to print the error; update
any references to response.error to use the exception handling flow instead.

[Aryan31v]

Checking in on this PR. I have updated the code to follow the correct auth pattern (removing .execute() and using direct response handling) and fixed the indentation as suggested. Ready for a final review.