Lambda scalability for an API is awful; it can't run concurrent requests (of course PHP largely can't do this either). An ECS service with pretty much any other language (for async/multithreaded runtimes) will scale far better.
A single minimal ECS instance can handle thousands of concurrent requests with an async runtime without running into so many cold starts that your p25 time is in the hundreds of ms.
1000 lambdas with 1000 database connections is also going to be a horrible way to do things on the backend. Add in the cost of RDS proxy for lambda and the ECS solution becomes even better.