I believe that is known as a "spring cassette." There are different types/models. If you do a Google search for "door handle round spring cassette," you should find some. Also, if you can actually access the metal spring inside, they sell replacement spring kits. I'm afraid that's about all I can offer, but maybe it will help your search.

https://www.doorhandlesprings.co.uk/collections/upvc-door-handle-springs/products/eurofix-rose-spring-cassette-used-in-hafele-and-other-lever-on-rose-door-handles

https://www.amazon.com/Handle-Spring-2-5-turn-circlips-Northern/dp/B007BS4O7O