Enable publishing for packages previously excluded from Docs MS (#31207)

Fixes #26770 

I have tested and validated that these packages will work with the new
`type2docfx` docs build system and this PR enables docs.ms publishing.

@xirzec -- When searching through `ci.yml` files I noticed two places
where we intentionally skip publishing docs on docs.ms:

*
https://github.com/Azure/azure-sdk-for-js/blob/main/sdk/communication/ci.yml#L64-L69
*
https://github.com/Azure/azure-sdk-for-js/blob/main/sdk/test-utils/ci.yml#L32-L49

In both of these instances these are `@azure-tools/___` packages. I left
these untouched. Should docs be published for these on
docs.microsoft.com whenever they release?

sdk/core/ci.yml

@@ -68,5 +68,3 @@ extends:
         safeName: azurecoresse
       - name: typespec-ts-http-runtime
         safeName: typespectshttpruntime
-        # TODO: Remove when REX validation tool is integrated: https://github.com/Azure/azure-sdk-for-js/issues/26770
-        skipPublishDocMs: true

sdk/identity/ci.yml

@@ -30,11 +30,8 @@ extends:
         safeName: azureidentity
       - name: azure-identity-cache-persistence
         safeName: azureidentitycachepersistence
-        # TODO: Remove when REX validation tool is integrated: https://github.com/Azure/azure-sdk-for-js/issues/26770
-        skipPublishDocMs: true
       - name: azure-identity-broker
         safeName: azureidentitybroker
       - name: azure-identity-vscode
         safeName: azureidentityvscode
-        # TODO: Remove when REX validation tool is integrated: https://github.com/Azure/azure-sdk-for-js/issues/26770
         skipPublishDocMs: true