Sure, at some point you're going to be relying on some 3rd party somewhere. We use a VPS and not a bare-metal hand-installed rack, and we rely on an electrical company and not a hand-turned crank to power our servers. As far as email goes, It's simply not possible to self-host transactional email in 2024 if you want it to arrive in an inbox and not a permanent spam blackhole; this is a people problem and not a technical one. Likewise, another people problem is that it's not possible to accept money online without involving a 3rd party service like Fractured Atlas or Stripe or PayPal.
(Moving away from GitHub towards a self-hosted Git solution, and away from Google Groups to a self-hosted mailing list, is actually on our long-term todo list[1]).
All those things don't mean one can't run one's web app on a single tiny server, like we do. I still argue that outsourcing the basic fundamentals of one's web app, like the OS, runtime, or database to some cloud service, or resorting to flavor-of-the-month frameworks or containers, or doing silly things like using Javascript to render one's entire frontend, often simply result in complexity, slowness, and bloat.
[1] https://github.com/standardebooks/web/blob/master/README.md#...