How can I use Gradle's configuration avoidance API to migrate a small application's build logic without causing downtime during the transition?

Consider a small Java application built with Gradle 8.x that currently uses eager project configuration in its build scripts. The team wants to adopt Gradle's configuration avoidance APIs (such as {@code Provider}, {@code Property}, and lazy task inputs) to improve build performance and enable future enhancements. The application must remain available to users throughout the migration, meaning no full rebuild or restart that would interrupt service.

What constraints and uncertainties should be evaluated when replacing eager configuration with lazy equivalents in this context? How can the migration be structured so that the build continues to produce correct artifacts while the changes are being introduced incrementally?