Convert API to AWS Lambda

Currently, the API runs as a full service. This is inefficient, considering what it does.

We should ensure the solution can run as a 'serverless' function, particularly an AWS Lambda function. This will allow us to run the API at a much-reduced cost.

NB: This does not need to include any IAC changes (if required).

Start by locating the current API service entry point and tracing how requests are handled, then identify the boundary needed for an AWS Lambda function. Done means the API can run as a serverless AWS Lambda function; infrastructure-as-code changes are explicitly out of scope.

Written by the indexing model from the issue text.