Should thunderfx's splitter reach executor level while determining if thunder can execute an operation

Nobody has claimed this yet.

The earlier assumption of `try_execute_thunder_symbol` (in splitter) only invokes the meta function associated with the Torch symbol (without interacting with the executors). But in order to fix https://github.com/Lightning-AI/lightning-thunder/issues/2036, the `value_and_grad` is added in `try_execute_thunder_symbol` to determine if the backward pass of an operator can be run by Thunder or not. However in the `value_and_grad` it introduces the interaction with executor binding:
[lightning-thunder/thunder/core/transforms.py](https://github.com/Lightning-AI/lightning-thunder/blob/f73bfa0eef857532beeaea44964b0bfd9926325a/thunder/core/transforms.py#L1492-L1507)
This Issue is created to discuss whether thunderfx's splitter should reach executor level while determining if thunder can execute an operation

_Originally posted by @kshitij12345 in https://github.com/Lightning-AI/lightning-thunder/issues/2073#issuecomment-2886039404_

cc: @kshitij12345 @IvanYashchuk

Start by reading thunder/core/transforms.py at lines 1492-1507, focusing on try_execute_thunder_symbol and its value_and_grad interaction with executor binding. Review the linked issue 2036 and the earlier issue 2073 discussion to determine whether splitter executor access is intended; done means reaching a documented decision on that design question.

Written by the indexing model from the issue text.