Test github token before running release script (#17562)

This stops people from getting half way through a step and it failing
due to the github token having expired (this happens to me every damn
time).

changelog.d/17562.misc

@@ -0,0 +1 @@
+Test github token before running release script steps.

scripts-dev/release.py

@@ -324,6 +324,11 @@ def tag(gh_token: Optional[str]) -> None:
 def _tag(gh_token: Optional[str]) -> None:
     """Tags the release and generates a draft GitHub release"""
 
+    if gh_token:
+        # Test that the GH Token is valid before continuing.
+        gh = Github(gh_token)
+        gh.get_user()
+
     # Make sure we're in a git repo.
     repo = get_repo_and_check_clean_checkout()
 
@@ -418,6 +423,11 @@ def publish(gh_token: str) -> None:
 def _publish(gh_token: str) -> None:
     """Publish release on GitHub."""
 
+    if gh_token:
+        # Test that the GH Token is valid before continuing.
+        gh = Github(gh_token)
+        gh.get_user()
+
     # Make sure we're in a git repo.
     get_repo_and_check_clean_checkout()
 
@@ -460,6 +470,11 @@ def upload(gh_token: Optional[str]) -> None:
 def _upload(gh_token: Optional[str]) -> None:
     """Upload release to pypi."""
 
+    if gh_token:
+        # Test that the GH Token is valid before continuing.
+        gh = Github(gh_token)
+        gh.get_user()
+
     current_version = get_package_version()
     tag_name = f"v{current_version}"
 
@@ -555,6 +570,11 @@ def wait_for_actions(gh_token: Optional[str]) -> None:
 
 
 def _wait_for_actions(gh_token: Optional[str]) -> None:
+    if gh_token:
+        # Test that the GH Token is valid before continuing.
+        gh = Github(gh_token)
+        gh.get_user()
+
     # Find out the version and tag name.
     current_version = get_package_version()
     tag_name = f"v{current_version}"
@@ -711,6 +731,11 @@ def _announce() -> None:
 @cli.command()
 @click.option("--gh-token", envvar=["GH_TOKEN", "GITHUB_TOKEN"], required=True)
 def full(gh_token: str) -> None:
+    if gh_token:
+        # Test that the GH Token is valid before continuing.
+        gh = Github(gh_token)
+        gh.get_user()
+
     click.echo("1. If this is a security release, read the security wiki page.")
     click.echo("2. Check for any release blockers before proceeding.")
     click.echo("    https://github.com/element-hq/synapse/labels/X-Release-Blocker")