If you're just getting started with DTM, I'd suggest looking into Launch, by Adobe. DTM is considered a legacy product with no new features planed. Launch is Adobe's new tag management solution and actually will work much better for your use case.
Angular is typically used with single page apps and DTM was designed before single page apps had really taken off. Launch on the other hand was build with SPA in mind. Like DTM, Launch is included for all Experience Cloud customers at no additional cost. If you want to get started with Launch, we've got some great resources on the Launch, by Adobe community.