Any kind of issue tracker or backlog management system which is worth it's bucks will allow you to customize the related work item types.
For example, for Azure Devops, I found this here in the docs. That's probably better than shoehorning technical tasks into the predefined user-centric work item types.
Said that, I think the option of putting "technical debt issues" into the backlog should not be overused. Each "clean-up task" should finally have the goal to allow smoother feature development or easier bugfixing on follow-up tasks. If you cannot name the purpose of such a clean-up task from the point of view of a feature or user story, chances are high the clean-up will never happen. Most technical issues can be worked on during feature development or bug fixing following the "boy scout rule".
That does not mean you should never make use of a "tech-debt" work item, but use them sparely and with care.