That is - something like this:

const app = new azure.appservice.AppService(`as`, {
    ...resourceGroupArgs,
    appServicePlanId: appServicePlan.id,
    siteConfig: {
        linuxFxVersion: "DOCKER|nginx"
    },
    appSettings: {
        "WEBSITE_RUN_FROM_ZIP": codeBlobUrl,
        "ApplicationInsights:InstrumentationKey": appInsights.instrumentationKey,
        "APPINSIGHTS_INSTRUMENTATIONKEY": appInsights.instrumentationKey
    },
    connectionStrings: [{
        name: "db",
        value: 
            pulumi.all([sqlServer.name, database.name]).apply(([server, db]) => 
                `Server=tcp:${server}.<http://database.windows.net;initial|database.windows.net;initial> catalog=${db};user ID=${username};password=${pwd};Min Pool Size=0;Max Pool Size=30;Persist Security Info=true;`),
        type: "SQLAzure"
    }]    
});

(building on the AppService example at https://github.com/pulumi/examples/blob/6852169b91da1d9de6912656fead3a355d6c57a3/azure-ts-appservice/index.ts#L4)

I think I was also looking at it from

new azure.appservice.FunctionApp

. I guess I can build the function app up from the AppService with the proper settings