chore(NODE-6243): move Node release tooling to drivers-github-tools

[baileympearson]

Description

What is changing?

Relies on mongodb-labs/drivers-github-tools#45. ✅

This PR adjust the driver's release to use shared release tooling for the node team from drivers-github-tools/node.

It turns out that sharing workflows requires workflow files to be put in the .github/workflows folder. So unless we want to have node-specific release actions in the .github/workflows folder in drivers-github-tools, we can't re-use workflows as a whole. I chose not to shared workflows and instead generate release files (see the generation script in drivers-github-tools).

Once mongodb-labs/drivers-github-tools#45 merges, I will update this PR so that it no longer points to my fork. ✅

Example GHA run: https://github.com/mongodb/node-mongodb-native/actions/runs/9700110739

Is there new documentation needed for these changes?

What is the motivation for this change?

Release Highlight

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Double check the following

• Ran npm run check:lint script
• Self-review completed using the steps outlined here
• PR title follows the correct format: type(NODE-xxxx)[!]: description
  • Example: feat(NODE-1234)!: rewriting everything in coffeescript
• Changes are covered by tests
• New TODOs have a related JIRA ticket

[evergreen-ci-prod]

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[nbbeeken]

Lgtm feel free to merge