I've heard one way to acheive this is by using api proxies/gateways. you can store secrets in a vault if you wish, but with a proxy, your app makes requests as usual without using secrets, its requests are then intercepted by the proxy to add authentication information transparently.

The added benefit is that you can also manage things like api rate limits, and implement all sorts of cool monitoring and api-specific threat detection centrally. I don't know of a way to do this outside of cloud provider services though.

Architecturally speaking, you have an environment that is at the same level of trust with respect to the data it processes, anything in there is unsecured, but all interactions outside of the system passes through a gateway proxy that manages all of what i mentioned earlier, including secret management.