Trim the migration guide to genuine v1-to-v2 breaking changes

The guide had accumulated entries that are not v1-to-v2 migration
items: new v2 feature notes, spec-adoption commentary, deprecations of
APIs that still work, and internal fixes with nothing for a migrator
to change. Remove those, including the whole Deprecations and
"Notes for 2026-era connections" groups.

Correct code that was wrong for v1.x or stale for current main, and
verify every remaining before/after example against the v1.x and main
trees. Fold closely related entries together (dependency requirements,
default server identity, direct calls to MCPServer's protocol methods,
the in-memory testing helper), standardize on the documented
`from mcp.server import MCPServer` import, regenerate the index and
suggested-order blocks to match, and cut history and over-explanation
throughout.

No-Verification-Needed: documentation-only change

Author: maxisbey