Removes hardcoded authContext in fetchProjectDeploymentDetails in favor of similar logic used in web-admin/src/routes/[organization]/[project]/+layout.svelte.

This fix should stop queries from being reset (and thus cancelled when inflight) by preventing invalidateRuntimeQueries from running as part of the setRuntime method of the runtime store.

This is a patch fix. The existing sequencing requires a thoughtful overhaul.

Checklist:

• Covered by tests
• Ran it and it works as intended
• Reviewed the diff before requesting a review
• Checked for unhandled edge cases
• Linked the issues it closes
• Checked if the docs need to be updated. If so, create a separate Linear DOCS issue
• Intend to cherry-pick into the release branch
• I'm proud of this work!