Remove packages.lock.json & fix CI caching

[Xtansia]

Description

Remove packages.lock.json as they generally are more effort to maintain than they offer in benefits. Fix caching in CI builds as previously nuget cache was being immediately wiped after being restored.

By submitting this pull request, I confirm that my contribution is made under the terms of the Apache 2.0 license.
For more information on following Developer Certificate of Origin and signing off your commits, please check here.

[opensearch-trigger-bot]

The backport to 1.x 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-1.x 1.x
# Navigate to the new working tree
cd .worktrees/backport-1.x
# Create a new branch
git switch --create backport/backport-265-to-1.x
# Cherry-pick the merged commit of this pull request and resolve the conflicts
git cherry-pick -x --mainline 1 6342e38b90c9c66b67246b816d9920d0e7ea0a72
# Push it to GitHub
git push --set-upstream origin backport/backport-265-to-1.x
# Go back to the original working tree
cd ../..
# Delete the working tree
git worktree remove .worktrees/backport-1.x

Then, create a pull request where the base branch is 1.x and the compare/head branch is backport/backport-265-to-1.x.