* Rewrite the v4 What's New page
Teach the headline features with code instead of asserting them, drop the
major-version throat-clearing and SEP list, and correct the elicitation
claim: ctx.elicit() is unchanged and handshake-only, while sampling and
roots are removed outright.
* Fix broken doc links and stale version references
Repoint five dead links and anchors, refresh v3-era version examples on the
v4 docs, and add the missing FastMCP 3 entry to the installation page's
upgrade section.
* Document server extensions
add_extension() shipped in v4 with no documentation page. Covers the
extension interface, request methods, tool-call interception, lifespan
ownership, and the client half.
* Link the FastMCP TypeScript library
* Address Codex review feedback
Gate the extension interceptor on the client's per-request opt-in rather
than claiming negotiation does it; show the v4 beta pin on the install
page instead of a version a reader cannot get; note that UserSession
requires authentication.