This commit uses the infer package to generate the schema. The hand-written schema has
moved to `legacy-schema.json`. `legacy-schem.json` is still embedded in the binary, since
the wrapped RPC provider still needs to be able to produce a schema. As resources are
moved over the raw RPC provider to infer, they can be removed from the legacy
schema. While it looks like the new `schema.json` file checked in with this commit is
extremely different, there are no semantic changes. The only changes are introducing the
module format key, re-ordering `"required"` and `"requiredInputs"` and adding the `"type":
"object",` indicator on objects (the default). For completeness, I have included the
entire diff:

```
$ json-diff original-schema.json schema.json
 {
+  meta: {
+    moduleFormat: "(.*)"
+  }
   types: {
     pulumiservice:index:DeploymentSettingsGitAuthBasicAuth: {
       required: [
+        "password"
         ...
-        "password"
       ]
     }
     pulumiservice:index:GCPOIDCConfiguration: {
       required: [
         ...
-        "workloadPoolId"
         ...
         ...
+        "workloadPoolId"
       ]
     }
     pulumiservice:index:AzureOIDCConfiguration: {
       required: [
         ...
+        "subscriptionId"
         ...
-        "subscriptionId"
       ]
     }
   }
   resources: {
     pulumiservice:index:AgentPool: {
+      type: "object"
     }
     pulumiservice:index:AccessToken: {
+      type: "object"
       required: [
+        "description"
         ...
-        "description"
         ...
       ]
     }
     pulumiservice:index:Team: {
+      type: "object"
       required: [
+        "members"
         ...
         ...
-        "members"
       ]
     }
     pulumiservice:index:TeamAccessToken: {
+      type: "object"
       required: [
         ...
+        "organizationName"
         ...
-        "organizationName"
         ...
       ]
       requiredInputs: [
         ...
+        "organizationName"
         ...
-        "organizationName"
       ]
     }
     pulumiservice:index:OrgAccessToken: {
+      type: "object"
     }
     pulumiservice:index:Webhook: {
+      type: "object"
       required: [
         ...
         ...
+        "format"
+        "name"
         ...
         ...
-        "name"
-        "format"
       ]
     }
     pulumiservice:index:DeploymentSettings: {
+      type: "object"
       requiredInputs: [
         ...
         ...
+        "sourceContext"
         ...
-        "sourceContext"
       ]
     }
     pulumiservice:index:StackTag: {
+      type: "object"
       required: [
+        "name"
         ...
         ...
         ...
-        "name"
         ...
       ]
       requiredInputs: [
+        "name"
         ...
         ...
         ...
-        "name"
         ...
       ]
     }
     pulumiservice:index:TeamStackPermission: {
+      type: "object"
       requiredInputs: [
-        "team"
         ...
+        "permission"
         ...
         ...
-        "permission"
+        "team"
       ]
     }
   }
 }
```