Ensure we dispose of the response stream in all cases

[stevejgordon]

Repeat calls to ExistsAsync can cause the connection limit to be reached as the optimized code which ensures we correctly handle cloud responses may not always run, leaving the response stream and therefore the connection open. This causes the default connection limit of 80 to be reached.

This fix ensures we correctly dispose of the response stream in all code paths.

Fixes #5775

[github-actions]

The backport to 7.13 failed:

The process '/usr/bin/git' failed with exit code 1

To backport manually, run these commands in your terminal:

# Fetch latest updates from GitHub
git fetch
# Create a new working tree
git worktree add .worktrees/backport-7.13 7.13
# Navigate to the new working tree
cd .worktrees/backport-7.13
# Create a new branch
git switch --create backport-5785-to-7.13
# Cherry-pick the merged commit of this pull request and resolve the conflicts
git cherry-pick --mainline 1 364ca23274e891edbca6473290100bbfc521dbbd
# Push it to GitHub
git push --set-upstream origin backport-5785-to-7.13
# Go back to the original working tree
cd ../..
# Delete the working tree
git worktree remove .worktrees/backport-7.13

Then, create a pull request where the base branch is 7.13 and the compare/head branch is backport-5785-to-7.13.