chore: Detect mismatch between `package.json` entrypoints and what our build step generates

I think we can use publint for this, but using the integration built into tsdown has a problem. Our current workflow is as follows:

• Build using tsdown
• Copy a slightly transformed package.json into dist/
• Publish the package

With the publint integration, it looks as follows:

• Build using tsdown
  • Running publint (❌ ERROR: package.json not found in dist/)
• Copy a slightly transformed package.json into dist/
• Publish the package

To make this work, we could move our package.json copying and transform as a step after tsdown finished building, and before publint runs. The version of tsdown we currently use doesn't expose this hook, but to update to another version of tsdown, it would be great if we were able to verify that the builds are correct. Therefore, this issue is blocked by #2420, which in turn is blocked by having better tests on built packages.

Start by reviewing the build workflow described in the issue and the built-package tests requested by #2420. Then trace how tsdown, the transformed package.json copy, and publint are invoked. Done means the generated package entrypoints can be checked successfully after the package metadata is present in dist/.