chore(ci): adopt trusted publishing

[rubiesonthesky]

PR Checklist

• Addresses an existing open issue: fixes 🛠 Tooling: release-it pipeline is not working #2487
• That issue was marked as status: accepting prs
• Steps in CONTRIBUTING.md were taken

Overview

Fixes (hopefully) release-it action. This is done after the examples pointed in the issue which are also same as in this PR: JoshuaKGoldberg/ts-api-utils#772

🐙

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 74.22%. Comparing base (dd16cfe) to head (82a2bfb).

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #2503   +/-   ##
=======================================
  Coverage   74.22%   74.22%           
=======================================
  Files         169      169           
  Lines        2875     2875           
  Branches      721      721           
=======================================
  Hits         2134     2134           
  Misses        508      508           
  Partials      233      233           

Flag	Coverage Δ
mutation	66.81% <ø> (ø)
unit	20.93% <ø> (ø)

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.
• 📦 JS Bundle Analysis: Save yourself from yourself by tracking and limiting bundle sizes in JS merges.

[JoshuaKGoldberg]

🤞. This looks about right. We'll see...

[rubiesonthesky]

Didn't work :( At least it's going further now but some bit is missing.

npm error code ENEEDAUTH
npm error need auth This command requires you to be logged in to https://registry.npmjs.org/
npm error need auth You need to authorize this machine using npm adduser
npm error A complete log of this run can be found in: /home/runner/.npm/_logs/2026-05-05T06_35_58_30