Still amazed that most ‘agile’ transformators/coaches have difficulty with waterfall and call it oldskool or ‘the past’. Most companies are best served with both! You should make agile and waterfall work together. They can!

It is often the case that waterfall projects need agile teams to deliver parts of the project. Since each method use their own prioritization (backlog vs project planning) they conflict often

This can be managed! Project Managers must understand they don’t manage the priorities on a backlog, its Product Owner is. Go to tactic is to pressure the PO to change the priorities in favor of the project.

They shouldn’t! Part of the project on an agile backlog should be prioritized on value like any backlog item. Most important is what value is and how it is defined. Project alignment should be part of this valuation and if done correctly will align agile with waterfall