docs: handle optional provider keys in setup check (bounty claim)

[MaxKerkula]

The quick setup check currently raises TypeError when OPENAI_API_KEY is absent, including an Anthropic-only setup. It also prints part of an OpenAI key when one is present.

This change reports whether each of the three documented provider keys has a nonempty value. It prints no key characters. The text explains that presence does not establish validity, and that unused providers can report False.

Validation: the exact Python block passes 54 isolated cases covering absent, empty, and synthetic nonempty values for all three providers, with and without a workspace value. The baseline fails in the Anthropic-only case. No real credentials or model API calls were used. git diff --check passes. This patch changes no links.

Link-check correction: CLI 4.2.876 reported 232 links in 70 files on native Windows for both trees. That output must not be treated as 232 established documentation defects. A fresh comparison on the same baseline checkout reports no broken links with Linux Node in WSL. An isolated fixture reproduces a Windows false positive for an existing nested page; the Linux check passes the valid fixture and fails its intentionally missing-page control. This is consistent with Mintlify issue #5680. Visual site rendering and external-link availability are separate checks.

Bounty claim: I request the Bronze tier under the documentation bounty program. This is one focused correction under 100 words. Please confirm eligibility and the award after review and merge. PayPal is my preferred payout method; payment details will be provided privately through a verified channel. No award or payment is assumed.

This contribution was prepared with AI assistance and checked locally.

Related: #65 proposed a similar correction and was closed, unmerged, by its author. The defect remains in the current base. These checks used the installed python-dotenv package with temporary synthetic .env files.