Update publish to skip private package (#40822)

Follow-up to https://github.com/vercel/next.js/pull/40815 ensures we
skip attempting to publish private packages like `next-swc`

x-ref:
https://github.com/vercel/next.js/actions/runs/3109438515/jobs/5039954716

packages/font/package.json

@@ -16,8 +16,5 @@
     "prepublishOnly": "cd ../../ && turbo run build",
     "dev": "tsc -d -w -p tsconfig.json",
     "typescript": "tsec --noEmit -p tsconfig.json"
-  },
-  "publishConfig": {
-    "access": "public"
   }
 }

scripts/publish-release.js

@@ -4,11 +4,12 @@
 const path = require('path')
 const { readdir } = require('fs/promises')
 const { execSync } = require('child_process')
+const { readJson } = require('fs-extra')
 
 const cwd = process.cwd()
 
 ;(async function () {
-  let isCanary = false
+  let isCanary = true
 
   if (!process.env.NPM_TOKEN) {
     console.log('No NPM_TOKEN, exiting...')
@@ -18,7 +19,10 @@ const cwd = process.cwd()
   try {
     const tagOutput = execSync('git describe --exact-match').toString()
     console.log(tagOutput)
-    isCanary = tagOutput.includes('-canary')
+
+    if (tagOutput.trim().startsWith('v')) {
+      isCanary = tagOutput.includes('-canary')
+    }
   } catch (err) {
     console.log(err)
 
@@ -72,6 +76,14 @@ const cwd = process.cwd()
   }
 
   for (const packageDir of packageDirs) {
+    const pkgJson = await readJson(
+      path.join(packagesDir, packageDir, 'package.json')
+    )
+
+    if (pkgJson.private) {
+      console.log(`Skipping private package ${packageDir}`)
+      continue
+    }
     await publish(packageDir)
   }
 })()