Website docs: improve navigation, accuracy, and command discovery

[SarthakWade]

Problem

The docs site is source-backed and visually consistent, but navigation depends on positional route slicing, command discovery is limited, and the overview incorrectly describes sessions as isolated even though normal sessions share cookies and storage.

Scope

• Replace positional route slicing with explicit navigation categories.
• Correct the session-isolation language using the documented profile contract.
• Add searchable or filterable command discovery without duplicating command definitions.
• Add stable section anchors, an in-page table of contents where useful, and clearer current-section state.
• Improve mobile navigation and keyboard accessibility while retaining the current typography, language, and visual system.
• Reserve Settings, Credentials, Profiles, and SDK sections, but publish claims only when their contracts ship.

Constraints

README, COMMANDS, SECURITY, phase contracts, package metadata, and benchmark results remain authoritative. New rendered claims must pass provenance validation. Do not add a parallel hand-maintained documentation source or redesign the site.

Acceptance criteria

• Every docs route is categorized explicitly and remains reachable on desktop and mobile.
• Search/filter behavior is keyboard accessible and tested.
• The inaccurate isolation claim is removed.
• Source-provenance validation rejects stale or duplicated feature claims.
• Web lint, build, responsive checks, and accessibility-focused tests pass.

[yashranaway]

Fine as parallel web work. Highest-value bit is killing the "sessions are isolated" claim. Command discovery should keep COMMANDS.md as the source. Do not invent Settings/Credentials/SDK pages until those contracts have shipped.

[yashranaway]

Implementation: #173.