Upgrade bun and @types/bun to 1.3.13 and consolidate to root-level dependency (#202)

### Why

Upgrades Bun from 1.3.11 to 1.3.13 across the monorepo.

### Details

`@types/bun` is now declared only at the root workspace level rather
than duplicated across individual packages (`brand`, `common`, `core`,
`cli`, and the adapter packages). This eliminates the version
fragmentation where some packages were pinned to 1.3.10 and others to
1.3.11, consolidating everything to a single 1.3.13 declaration.

### Verification

CI

<!-- CURSOR_SUMMARY -->
---

> [!NOTE]
> **Low Risk**
> Low risk lockfile/tooling update: bumps Bun and TypeScript typings and
removes per-package `@types/bun` declarations, with no runtime logic
changes. Main risk is CI/build differences due to the Bun/type upgrade
and dependency consolidation.
> 
> **Overview**
> Upgrades the repo’s Bun toolchain to `1.3.13` (updates `mise.toml`,
root `packageManager`, and `bun.lock`), including
`@types/bun`/`bun-types` to `1.3.13`.
> 
> Consolidates Bun typings to the root workspace by removing duplicated
`@types/bun` devDependencies from individual packages (e.g., `core`,
`common`, `cli`, `brand`, and adapter packages), and drops lockfile
entries that existed only for those package-scoped installs.
> 
> <sup>Reviewed by [Cursor Bugbot](https://cursor.com/bugbot) for commit
c5f8e1d. Configure
[here](https://www.cursor.com/dashboard/bugbot).</sup>
<!-- /CURSOR_SUMMARY -->

Author: eXamadeus

bun.lock

@@ -2,7 +2,7 @@
 TURBO_TEAM = "facets"
 
 [tools]
-bun = "1.3.11"
+bun = "1.3.13"
 node = "24.14.1"
 lefthook = "2.1.4"
 gh = "2.89.0"

mise.toml

@@ -2,7 +2,7 @@
   "$schema": "https://json.schemastore.org/package.json",
   "private": true,
   "type": "module",
-  "packageManager": "bun@1.3.11",
+  "packageManager": "bun@1.3.13",
   "workspaces": {
     "packages": [
       "packages/*",
@@ -37,7 +37,7 @@
     "@changesets/release-utils": "0.2.7",
     "@fission-ai/openspec": "1.3.0",
     "@octokit/auth-app": "8.2.0",
-    "@types/bun": "1.3.11",
+    "@types/bun": "1.3.13",
     "@types/node": "24.12.2",
     "dedent": "1.7.2",
     "mint": "4.2.521",

package.json

@@ -22,7 +22,6 @@
   },
   "devDependencies": {
     "@agent-facets/adapter": "workspace:*",
-    "@types/bun": "1.3.11",
     "arktype": "2.2.0",
     "tsdown": "^0.21.9",
     "typescript": "^6.0.3"

packages/adapters/claude-code/package.json

@@ -22,7 +22,6 @@
   },
   "devDependencies": {
     "@agent-facets/adapter": "workspace:*",
-    "@types/bun": "1.3.11",
     "tsdown": "^0.21.9",
     "typescript": "^6.0.3"
   },

packages/adapters/codex/package.json

@@ -22,7 +22,6 @@
   },
   "devDependencies": {
     "@agent-facets/adapter": "workspace:*",
-    "@types/bun": "1.3.11",
     "arktype": "2.2.0",
     "tsdown": "^0.21.9",
     "typescript": "^6.0.3"

packages/adapters/opencode/package.json

@@ -21,9 +21,6 @@
     "types": "tsc --noEmit",
     "test": "bun test"
   },
-  "devDependencies": {
-    "@types/bun": "1.3.10"
-  },
   "peerDependencies": {
     "typescript": "^5 || ^6"
   },

packages/brand/package.json

@@ -37,7 +37,6 @@
     "@agent-facets/core": "workspace:*",
     "@agent-facets/adapter": "workspace:*",
     "@agent-facets/adapter-opencode": "workspace:*",
-    "@types/bun": "1.3.10",
     "ink-testing-library": "4.0.0"
   },
   "peerDependencies": {

packages/cli/package.json

@@ -8,8 +8,5 @@
   "scripts": {
     "types": "tsc --noEmit",
     "test": "bun test"
-  },
-  "devDependencies": {
-    "@types/bun": "1.3.10"
   }
 }

packages/common/package.json

@@ -29,7 +29,6 @@
   "devDependencies": {
     "@agent-facets/common": "workspace:*",
     "@agent-facets/adapter": "workspace:*",
-    "@types/bun": "1.3.10",
     "tsdown": "^0.21.9",
     "typescript": "^6.0.3"
   },