This feels very "Serverless is cool, everyone is saving money on it, lets do the same"

> I only had to add a simple config file, add one dependency and one small startup class to my existing API project.

This is not the way to do it, you have to spend some time on lambda approach.

Usually splitting up your code in to smaller chuncks so you don't end up with long spool up times and you can do things like keeping your lambda warm and caching high impact parts of the code. (sometimes of course you can't cache, I know)

Having gone through this process myself with a very very large code base, it would have not worked to just slap it into serverless.

Going server less can save you money, but not by just taking your existing app and throwing it on Lambda.