I am trying to integrate datadog log monitoring with strapi, logging works but the injection doesnt work

Make a server.js file in your root dir. and put this in it.

const tracer = require('dd-trace').init({
  appsec: true
  // any options you need
})
const strapi = require('@strapi/strapi');
const app = strapi({ distDir: './dist' });
app.start();

Start strapi with:

node server.js

Don’t forget to install dd-trace.
(Edit:) I suggest that you install @strapi-logger and setup Winston (a guide is on the Strapi docs)

Here’s the working stats in Datadog: