feat(settings): Workspace PATH section in the Tools category (T-511)

The UI half of D-106 (D-6 parity with `clide env path`): an ordered
preset editor — add/remove/reorder, a missing-dir warning, a worktree
note naming the shared main repo, and capture-from-login-shell
suggestions adopted with one click. Writes land on the same user-scope
key the CLI verbs use and publish on the same channel, so both
surfaces stay live off the store notifier.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

assets/i18n/en_us/builtin.tools-settings.json

@@ -7,5 +7,20 @@
   "settings.field.d2.label": { "translation": "d2" },
   "settings.field.d2.help": { "translation": "Absolute path to the d2 diagram compiler; blank to auto-resolve." },
   "settings.field.detect.label": { "translation": "Re-detect" },
-  "settings.field.detect.help": { "translation": "Re-scan PATH and the common install dirs, overwriting the paths above." }
+  "settings.field.detect.help": { "translation": "Re-scan PATH and the common install dirs, overwriting the paths above." },
+  "settings.section.path": { "translation": "Workspace PATH" },
+  "settings.field.pathPreset.label": { "translation": "Prepend to PATH" },
+  "settings.field.pathPreset.help": { "translation": "Directories put ahead of PATH in Claude sessions and terminal panes spawned for this repo; worktrees share the repo's preset. Applies to new shells." },
+  "path.noWorkspace": { "translation": "Open a workspace to set its PATH preset." },
+  "path.sharedRoot": { "translation": "Worktree — preset shared with" },
+  "path.empty": { "translation": "No preset entries — spawned shells get the resolved login-shell PATH as-is." },
+  "path.add": { "translation": "Add entry" },
+  "path.invalid": { "translation": "Enter an absolute path (or ~/…)." },
+  "path.missing": { "translation": "missing" },
+  "path.moveUp": { "translation": "Move up" },
+  "path.moveDown": { "translation": "Move down" },
+  "path.remove": { "translation": "Remove" },
+  "path.capture": { "translation": "Suggest from login shell" },
+  "path.captureNone": { "translation": "Nothing to suggest — the login-shell PATH is already covered." },
+  "path.addSuggestion": { "translation": "Add suggested entry" }
 }

assets/i18n/nl_nl/builtin.tools-settings.json

@@ -7,5 +7,20 @@
   "settings.field.d2.label": { "translation": "d2" },
   "settings.field.d2.help": { "translation": "Absoluut pad naar de d2-diagramcompiler; leeg om automatisch te bepalen." },
   "settings.field.detect.label": { "translation": "Opnieuw detecteren" },
-  "settings.field.detect.help": { "translation": "Scan PATH en de gangbare installatiemappen opnieuw; overschrijft de paden hierboven." }
+  "settings.field.detect.help": { "translation": "Scan PATH en de gangbare installatiemappen opnieuw; overschrijft de paden hierboven." },
+  "settings.section.path": { "translation": "Workspace-PATH" },
+  "settings.field.pathPreset.label": { "translation": "Vooraan aan PATH toevoegen" },
+  "settings.field.pathPreset.help": { "translation": "Mappen die vóór PATH komen in Claude-sessies en terminalvensters voor deze repo; worktrees delen de preset van de repo. Geldt voor nieuwe shells." },
+  "path.noWorkspace": { "translation": "Open een workspace om de PATH-preset in te stellen." },
+  "path.sharedRoot": { "translation": "Worktree — preset gedeeld met" },
+  "path.empty": { "translation": "Geen preset-items — nieuwe shells krijgen het opgeloste login-shell-PATH ongewijzigd." },
+  "path.add": { "translation": "Item toevoegen" },
+  "path.invalid": { "translation": "Voer een absoluut pad in (of ~/…)." },
+  "path.missing": { "translation": "ontbreekt" },
+  "path.moveUp": { "translation": "Omhoog" },
+  "path.moveDown": { "translation": "Omlaag" },
+  "path.remove": { "translation": "Verwijderen" },
+  "path.capture": { "translation": "Voorstellen uit login-shell" },
+  "path.captureNone": { "translation": "Niets voor te stellen — het login-shell-PATH is al gedekt." },
+  "path.addSuggestion": { "translation": "Voorgesteld item toevoegen" }
 }