I didn't used Play Framework so I'm not familiar with it's architecture. But I found your question interesting and did some research.
Twirl Template Engine with Spring MVC Demo App
But I did found some useful resources that might help your case.
Spring MVC Twirl GitHub
This repository has an identical example of what you're looking for.
To be honest, I haven't tried to run this code myself but it seems like a trustworthy user.
Also, I did found a Blog Example which explains how to run Twirl Template Engine standalone without Play Framework. This doesn't cover your use-case but it suggests it's possible to use Twirl Template Engine without Play Framework (hence with right configs it's possible to use it with Spring)
Standalone Twirl Template Engine Usage Example - Blog and GitHub Repo
Standalone Twirl Template Engine Usage
Standalone Twirl Template Engine Usage GitHub Repository
Different Template Engines for Spring - Does not mention Twril
Also, if you wan't a great reading reference I always visit Baeldung website
I found a blog post about different template engines for Spring. They don't cover your use case, but based on this article it is possible to use variety of different engines given that you have proper dependency (e.g. maven, gradle) and do a proper configuration.
Does not mention Twirl, but it might give you some idea how to do it
Template Engine for Spring Blog Post