Starter budget and the client list: each spawned forge carries a spending ceiling, and the parent lists who was sent what #601

Pillar: P4 Forge in a link (umbrella #590). One run, started fresh from today's main.

Outcome (what a person sees). When the owner makes a forge for someone, he sets a starter budget, and one page lists every forge he has sent: for whom, which apps, the link, whether they have logged in, and what has happened since.

Today. The parent keeps one ledger line per child (<data>/spawn/<name>.json); nothing reads it back for a person, and the plan carries no budget.

Acceptance.

• [ ] Spawn input takes budgetUsd (default 20) and for (free text: the person, client or organization). The child's repositories start with that autonomy ceiling, and the child's board says "Starter budget: $X of $Y spent".
• [ ] /forges (owner only): one row per child from the ledger: name, for whom, apps sent, link, claimed or not, last activity. Claimed and last activity come from a small public GET /api/v1/forge on the child ({claimed, lastActivityAt}, nothing else); "unknown" when it cannot be reached.
• [ ] Reached from the feed's header in two taps, and from the "+ New forge" page (#426) when it lands.

Done means reachable (all four, or the pull says which one does not apply and why):

• Page: /forges
• MCP: a forges tool returns the same rows
• Test: ledger rows render; budget reaches the child's ceiling; unreachable child reads unknown
• Look: the page with two children, on the pull

Start from: src/actions/spawn.ts, src/spawn/plan.ts, docs/SPAWN.md, src/http/api.ts, src/http/mcp.ts, src/web/pages/settings.ts.

Depends on: #577 (spawn's API and MCP callers, pull #581).

Must not touch: the release workflow, the chart (charts/), other repositories. Do not change how a child is placed or copied.

Added acceptance (owner's contract rule, now in the direction and docs/VISION.md):

• [ ] Contract: one interface per job. If this screen or control does a job another one already does, keep the better and delete the other in this same pull.
• [ ] Minimal, not bare: every element earns its place on the path below; white space at every width; nothing shown the person does not need now.
• [ ] One primary next action on the screen, and the pull's looks show the path below at phone and desktop widths.
• [ ] The pull says what it removes for every screen or control it adds.

The path: the owner, from the feed's header, checks on forges he sent; the one primary action per row is open its link; he goes to the child or back to the feed.

Split: this issue is now the whole-life starter budget (pull #765). The client list is #776. The spawn input that puts a budget on a child's starter key follows once #747 (the key) merges.