Investigate speeding up CodeBuild processes

[cdriehuys]

The CodeBuild processes for building the API Docker image and building/testing the web application are the slowest parts of the build process. Through a mixture of caching and custom Docker images, we should be able to speed these processes up.

When building the Docker image, we could look into caching the intermediate layers of the image between runs so that they can be reused.

For building/testing the API, we spend a lot of time installing system and node dependencies for Cypress, our testing framework. By using one of their provided Docker images, we could greatly speed up our build times. Additionally, caching node_modules between runs would also speed up the build.