const pgContainer = new docker.Container('postgres-container', { ... })
const apiContainer = new docker.Container('api-container', {
    ...,
    envs: [
        pulumi.interpolate`DB_HOST=${pgContainer.networkDatas[0].gateway}`,
    ]
}, { dependsOn: [pgContainer] })

apply

.apply(x => console.log(x)

pgContainer.networkDatas[0].gateway.apply(x => x)

import * as pulumi from "@pulumi/pulumi";
import * as docker from "@pulumi/docker";

const pgContainer = new docker.Container("postgres-container", {
  image: "pg-image",
});
const apiContainer = new docker.Container("api-container", {
  image: "api-image",
  envs: [pulumi.interpolate`DB_HOST=${pgContainer.networkDatas[0].gateway}`],
});