docs: clarify when Client(raise_exceptions=True) actually raises

[HaoChiBao]

Summary

• Document the real semantics of Client(raise_exceptions=True): in-memory only; still raises MCPError on unexpected handler crashes, but unsanitises the message and chains __cause__; does not turn tool is_error=True into an exception; ignored for URL/transport clients; drop on mode="legacy".
• Expand Testing, with cross-links from Clients, Troubleshooting, and the low-level server page; replace the Client.raise_exceptions TODO with a docstring that matches that behaviour.
• Add docs_src/testing/tutorial002.py plus docs_src tests covering the True/False contrast.

Fixes #3287.

AI disclosure

This contribution was prepared with AI assistance (Cursor). A human reviewed the traced behaviour and the docs/tests before opening the PR.

Test plan

• uv run --frozen ruff format / ruff check on touched Python files
• Relevant docs_src and client raise_exceptions tests (7 passed)
• Confirm docs render for Testing / Troubleshooting / Clients "In tests"
• No runtime behaviour change intended

[github-actions]

This PR has been closed automatically. It's still a draft, but we close those early so you don't put in more time only to have it closed the moment you mark it ready.

This repo only keeps pull requests open when they come from a maintainer, or from a contributor a maintainer has assigned to the linked issue, and you aren't currently assigned to #3287.

If a maintainer assigns you to #3287, this PR reopens on its own and there's nothing more you need to do here. Assignment is a maintainer call based on capacity; comments that only ask to be assigned don't factor in. What does help is engaging on the issue itself by confirming the repro, explaining why it matters for your use case, or describing the approach you'd take.

You're welcome to keep pushing commits here (just avoid force-pushing, since GitHub can't reopen a rewritten branch), but that on its own won't get the PR reviewed or the issue assigned, and realistically most auto-closed PRs stay closed. There's no need to open a new PR either way.

CONTRIBUTING.md has the full reasoning, but in short:

• We're a small team with very little capacity to review community PRs right now.
• Many recent PRs are AI-generated with little human review, and reviewing one carefully still costs a maintainer as much time as it ever did. A well-described issue is usually more useful to us than the code.

Maintainers: reopen, remove missing-issue-link, or add bypass-issue-check to override.