feat(lanes): lane runtime UI, docs, and env additions (A1+A2)

Client-side rendering for the per-lane runtime facts (slot, ports,
database, Redis index, service liveness) added in the server-side
A1/A2 work, plus the doc updates (README, CLAUDE.md, docs/API.md,
client/server READMEs) describing the new profile.env keys, hook
environment contract, and REST endpoints.

client/src/i18n/locales/en/lanes.json

@@ -19,7 +19,6 @@
   "addLaneTitlePlaceholder": "Optional",
   "autoStage": "auto: {{stage}}",
   "cardId": "Lane {{id}}",
-  "stageUndeclared": "not declared",
   "confirmRemoveCancel": "Cancel",
   "confirmRemoveConfirm": "Remove",
   "confirmRemoveMessage": "This action cannot be undone.",
@@ -65,6 +64,17 @@
   "moreActions": "More actions",
   "preflightError": "Could not load the current lane facts.",
   "preflightErrorWithMessage": "Could not load the current lane facts: {{message}}",
+  "runtime.boot": "▶ up",
+  "runtime.busy.down": "stopping…",
+  "runtime.busy.up": "booting…",
+  "runtime.down": "down",
+  "runtime.healthy": "healthy",
+  "runtime.partial": "partial",
+  "runtime.slot": "slot {{slot}}",
+  "runtime.steppedAsideTitle": "Stepped aside from {{expected}}, which was already in use",
+  "runtime.stop": "■ down",
+  "runtime.toggleTitle": "Boot or stop this lane's own application stack (separate from its Claude run)",
+  "stageUndeclared": "not declared",
   "status.failed": "failed",
   "status.idle": "idle",
   "status.provisioning": "provisioning",