Sync eng/common directory with azure-sdk-tools for PR 12418 (#3155)

Sync eng/common directory with azure-sdk-tools for PR
Azure/azure-sdk-tools#12418 See [eng/common
workflow](https://github.com/Azure/azure-sdk-tools/blob/main/eng/common/README.md#workflow)

Co-authored-by: Ben Broderick Phillips <[email protected]>

Author: azure-sdk

eng/common/instructions/azsdk-tools/typespec-to-sdk.instructions.md

@@ -33,7 +33,7 @@ Wait for the user to respond with a confirmation before proceeding to Step 1. Us
 1. Run `azsdk_get_github_user_details` to verify login status
 2. If not logged in, prompt: "Please login to GitHub using `gh auth login`"
 3. Once logged in, display user details to confirm identity
-4. Run `azsdk_check_typespec_project_in_public_repo` to verify repository
+4. Run `azsdk_typespec_check_project_in_public_repo` to verify repository
 5. If not in public repo, inform: "Please make spec changes in Azure/azure-rest-api-specs public repo to generate SDKs"
 **Success Criteria**: User authenticated and working in public Azure repo
 
@@ -113,4 +113,4 @@ Wait for the user to respond with a confirmation before proceeding to Step 1. Us
 2. Inform user to approve the package release using release pipeline.
 
 ## Process Complete
-Display summary of all created PRs and next steps for user.
+Display summary of all created PRs and next steps for user.