Removes deprecated set-output usage

For more information see
https://github.blog/changelog/2022-10-11-github-actions-deprecating-save-state-and-set-output-commands/

This change bumps a bunch of the internal actions packages. Note that
the only required version change is `actions/core` to 1.10.0. The others
are not required, but seem like a reasonable idea.

It also changes all of the workflows that use `set-output`.

node_modules/@actions/cache/package.json

@@ -1,6 +1,6 @@
 {
   "name": "@actions/cache",
-  "version": "3.0.4",
+  "version": "3.0.5",
   "preview": true,
   "description": "Actions cache lib",
   "keywords": [
@@ -37,7 +37,7 @@
     "url": "https://github.com/actions/toolkit/issues"
   },
   "dependencies": {
-    "@actions/core": "^1.2.6",
+    "@actions/core": "^1.10.0",
     "@actions/exec": "^1.0.1",
     "@actions/glob": "^0.1.0",
     "@actions/http-client": "^2.0.1",