Refactor build logic to emulate Vite Environment API

[markdalgleish]

While investigating a migration to Vite's environment API, it became clear that some elements of our architecture make this difficult. The biggest challenge is that our server bundle builds can't be expressed as different environment configs within the same plugin instance, instead relying on the fact that each server bundle build is a completely standalone Vite build.

This PR is a refactor to bring our architecture much closer to how the environment API works so the migration work is much simpler, while also making it feasible to maintain backwards compatibility for Vite 5 until our next major release. The ideal solution I'm aiming for is to emulate the environment API in our custom build setup.

[changeset-bot]

⚠️ No Changeset found

Latest commit: 2562286

Merging this PR will not cause a version bump for any packages. If these changes should not result in a new version, you're good to go. If these changes should result in a version bump, you need to add a changeset.

This PR includes no changesets

When changesets are added to this PR, you'll see the packages that this PR includes changesets for and the associated semver types

Click here to learn what changesets are, and how to add one.

Click here if you're a maintainer who wants to add a changeset to this PR