Remove trainer._device_type in favor of check Accelerator class

[four4fish]

Proposed refactor

Follow up for #11001: Generalize internal checks for precision plugin type, training type, accelerator type

Motivation

Code simplification

Pitch

After #11001, _device_type is not needed anymore

    @property
    def _device_type(self) -> _AcceleratorType:
        return self._accelerator_connector.

Instead in tests and where we need check device type, use

isinstance(trainer.accelerator, XAccelerator)

Additional context

---

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cc @justusschock @awaelchli @akihironitta

[awaelchli]

Hey @four4fish
Thanks for looking at this.
This is not something we need to deprecate because it's already declared as internal, not exposed to user.
It can simply be removed together with the last part of #10821

[four4fish]

Solved by #11992