[Feat]: Benchmark weights for the container-and-subname PoP lite registration path

[sphamjoli]

Component

Proof of Personhood

Priority

P1

Summary

Issuing a PoP lite username changed shape. Instead of minting one atomic label, the gateway path now
splits stem.suffix, mints the numeric container on first use, and records the stem as a subname
beneath it. This changes the on-chain work each Root-origin dispatch performs, so the weights that
gate that dispatch need re-measuring. Deferring the store write to settlement also moves work out of
the dispatch and into the settlement call, and that split needs measuring separately so neither side
is under-weighted.

Proposal

Benchmark the paths that changed and compare them against the previous atomic-label figures:

• Cold lite registration: split the label, mint the container (01), record the subname, and
  persist the chat key. This is the most expensive path because the container is minted here.
• Warm lite registration: the container already exists, so only the subname record and the chat key
  are written.
• Settlement: writing the deferred label into the owner's store at the subname node.

Produce weight and proof-size figures for each path using the previewnet-engine harness, record cold
and warm separately because the first username under a container costs more than the rest, and update
any weight definitions that gate the gateway dispatch from the measured figures.

Acceptance criteria

• Weight and proof size measured for cold lite registration, warm lite registration, and settlement.
• Figures compared against the previous atomic-label registration path.
• Cold and warm paths reported separately.
• Weight definitions that gate the gateway dispatch updated from the measured figures.