docs: set_many examples use dict, need list[FieldUpdate] (crashes)

[zeevdr]

Description

set_many() is documented and demonstrated with a plain dict, but the real signature requires list[FieldUpdate] and raises AttributeError at runtime (the body iterates u.field_path). It is wrong in sdk/docs/quickstart.md:54, sdk/docs/async.md:21, and in the runnable example examples/async-client/main.py:53-57 (CI stays green because the mock never exercises the path). No doc shows the correct FieldUpdate usage.

Acceptance criteria

• Fix set_many examples to use [FieldUpdate(...), ...] in docs and in examples/async-client/main.py.
• Add a Bulk writes subsection documenting FieldUpdate (including expected_checksum / value_description).
• Add a CI step that executes examples against a live or mocked server so a broken example fails.

Source: documentation review, 2026-06-07.