docs: correct the handler-cost figures — the 68ms warning is cold-start

[marselsel]

Re-validation of the three claims behind "the per-request registration cost stays" (finding #1 in #56). One of the numbers was wrong.

The wrong number

I cited Skybridge's boot warning — "The Skybridge handler took 68ms — it runs on every request" — as if 68ms were the recurring per-request cost in the container. It is not. That line prints exactly once, from the cold first build inside ready(), so it carries the JIT warm-up. grep -c "handler took" on the container log after 80 requests: 1.

Steady state over HTTP against the same image:

/status	2.1 ms
initialize	29.5 ms — builds all 53 tool schemas and uses none of them
tools/list	41.3 ms

So ~27 ms, matching the host measurement of ~23 ms rather than the 68 ms the warning suggests. The finding is unchanged in kind and about 2.5x smaller in size. Worth recording because the warning's own wording ("it runs on every request, so this cost is paid per request") is what invites the misreading — the sentence is true, the sample attached to it is not the steady-state one.

The container number also turned out to be ~the host number, so there is no hidden Cloud Run multiplier to worry about.

The two claims that held

zod does not memoize. The earlier check was three single samples with visible noise (9.5 / 2.6 / 5.6 ms — the third slower than the second, which should have made me look twice). Redone with 300 iterations at the SDK's actual conversion target (draft-2020-12, read out of JSON_SCHEMA_CONVERSION_TARGET):

A) same instance, converted repeatedly      median=0.84ms  (first call 7.12ms, call #300 0.92ms)
B) fresh z.object each time (today)         median=1.03ms
C) same reference returned twice?           false      <- a new object every call

Hoisting a z.object buys 18%, where a memo would buy ~100%.

A pre-built schema does not typecheck. Verified with tsc on a two-tool probe rather than by reading the type declarations:

error TS2769: No overload matches this call.
  Type 'ZodObject<{ id: ZodString; n: ZodOptional<ZodNumber>; }, $strip>' is not
  assignable to type 'Record<string, StandardSchemaWithJSON<unknown, unknown>>'.
    Index signature for type 'string' is missing in type 'ZodObject<...>'.
error TS2322: Type 'unknown' is not assignable to type 'string'.

The second error is the important one: forcing it through would type every handler argument unknown across all 53 tools.

Also confirmed skybridge@2.0.0 is still the newest published release, so none of this is already fixed upstream.

Scope

Comments and CHANGELOG only. No code, no behaviour change. 454 tests, typecheck clean.