You can do that, but it might be more work than it's worth.
First, you can obviously connect to your backend via an Ajax request and push data to the datalayer in your success callback. If you include an "event" key, you can fire tags in GTM accordingly. This is probably not what you mean, and it won't solve your problem.
For some time now, Google offers also a server-side Google Tag Manager. This is set up as a docker container in "the Cloud" (Google presumes GCP, but it will also run on AWS an everywhere else where you can run docker containers).
This server-side GTM receives http requests from your website (or other sources, such as your backend) and distributes them to one or more configured tags. This reduces the amount of code in the frontend, allows to rewrite javascript cookies to cookie headers (thereby evading tracking protection) an d allows for more privacy by redacting data before it is passend on to the marketing vendors.
Server-side GTM does not fully replace GTM, instead it is complementary: You probably want to keep your client-side GTM to set up triggers by which to send requests to the server-side part.
You can also use this to integrate backend services; the idea is that your service send a request to server-side GTM, where it is then cached and available to to be used in tags.
The (very much recommended) blog of Lukas Oldenburg has an example where this is used to stitch together user information, but the example could be adapted to other use cases: https://lukas-oldenburg.medium.com/use-google-tag-manager-server-side-for-visitor-stitching-by-querying-a-gcp-database-in-real-time-644001068a1c.
But that means you need to set up a cloud environment etc., not an unsurmountable amount of work, but not something you would do without a convincing business case, either.