Remove legacy methods used to break retain cycles

Some methods were introduced to break retain cycles. Try to remove them by analyzing dependency object graph and use weak references where needed.

Get rid of:
- [ ] `releasePushedViewController` methods
- [ ] Direct calls to `destroy` method

Start by mapping the dependency object graph around the `releasePushedViewController` methods and direct `destroy` calls. Identify where weak references are needed, then verify that both legacy method calls can be removed without reintroducing retain cycles or changing ownership behavior.

Written by the indexing model from the issue text.