The whole spiel of AWS (and GCP, Azure, etc.) is to hide the costs behind pricing tiers and service categories. You cannot pay a single price per service but you need to pay for bandwidth, requests, and disk space or computing time separately for each service.
Even AWS salespeople will not give you a price because it heavily depends on your usecase.
All cloud providers have calculator tools to give you a feeling about being informed but you can theorize as much as you want, reality will be different. There are just too many variables to consider.
I think for a lot of use-cases, a $5 droplet in DigitalOcean will be cheaper than paying for all these cloud APIs separately. (Although AWS does provide free-tier for many APIs your first year).
Now that I can afford more than $5 for side projects, I am looking for things like ease of deployment, reduced burden of maintenance etc. IMO serverless gives me this (once you have a proper setup of course). There are no machines to login to, no need to worry about patching hosts etc.
There was a time when my wordpress blog (RIP) used to get hacked every 6 months. A purely serverless model reduces the surface area for attacks.
I guess what I am trying to say is that for me personally, serverless is not about the immediate infra cost, but the TCO long term. And if/when your side projects take off, you can always go back to bare-metal servers as required.
Even AWS salespeople will not give you a price because it heavily depends on your usecase.