tabbox: Drop TabBoxClient

The indirection contributes unnecessary complexity. The usage of
std::weak_ptr and std::shared_ptr complicates the things further, e.g.

![Screenshot_20230325_170226](/uploads/d8b68a9eff47c93c4463bb230b5bbe49/Screenshot_20230325_170226.png)

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Ideally, same should be done with TabBox and TabBoxHandler, but that can be done in another MR.