📝 Correct the pi-lsp false-positive finding

The TS1295/TS1287 errors were not an LSP misconfiguration: the server
was still running from an earlier local test that had emptied
package.json, and kept the corrupted project state alive. Driven with
pi-lsp's exact handshake, tsc --lsp --stdio reads tsconfig.json
correctly. Record the real caveat instead: no file watchers, so
tsconfig.json/package.json edits can leave diagnostics stale until the
server restarts.

backlog.tasks

@@ -22,11 +22,11 @@ Setup:
     ☐ Fix the declaration emit (`.d.ts` post-step) or stop using relative `.ts` in the declaration surface
     ☐ Reconcile the README/CONTRIBUTING claim that `rewriteRelativeImportExtensions` yields "conventional ESM imports"
     ☐ Add a consumer-resolution test to the suite (durable guard; `attw` currently misses it)
-☐ Document pi-lsp false-positive diagnostics
-    - `lsp_diagnostics` reports TS1295/TS1287 "CommonJS file under `verbatimModuleSyntax`" errors that `check:tsc` never produces — the server is not picking up the repo's `tsconfig.json`
-    - AGENTS.md only warns that empty LSP output is inconclusive, not that it can emit false errors
-    ☐ Add a line to AGENTS.md: ignore LSP errors that `check:tsc` does not reproduce
-    ☐ Or fix the LSP server configuration so it picks up `tsconfig.json`
+✔ Document pi-lsp false-positive diagnostics @done
+    - `lsp_diagnostics` reported TS1295/TS1287 "CommonJS file under `verbatimModuleSyntax`" errors that `check:tsc` never produced
+    - root cause: an earlier local test emptied package.json; the still-running TS7 server (5 min idle timeout) kept the corrupted project state alive and reported it against the real files
+    ✔ No LSP misconfiguration to fix: driven with pi-lsp's exact handshake, tsc --lsp --stdio reads tsconfig.json correctly; hover resolves real inferred types and lsp_diagnostics is clean on a fresh server @done
+    ✔ Added the one real caveat to AGENTS.md: the server does not register file watchers, so tsconfig.json/package.json edits can leave diagnostics stale until it restarts @done
 ✔ Run packaging checks in CI `build` @done
     - `publish:publint` / `publish:attw` only run in the tag-triggered `publish` job, so a PR that breaks packaging stays green until release
     ✔ At minimum add `publish:publint` to the `build` job (offline, fast); `attw` needs a pack @done