Refactoring of the launcher

> Similar to the earlier conversations on this method (see below), this continues a pattern I've flagged before: accumulation of low-level, untested branching logic. I understand this follows the existing style of the method, but each addition makes the eventual refactor larger and the method harder to review as a whole.
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> I'd like to see argument-validation branches like this (and the timeout-string construction from before) extracted into small, testable methods rather than added inline. Given this has come up multiple times now, including in internal meetings, please treat this as a standing convention going forward, not a case-by-case judgment call.
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> Final changes to the same method in same PR:
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_Originally posted by @seanpearsonuk in [#4990](https://github.com/ansys/pyfluent/pull/4990/changes#r3550231986)_

The payload does not name a file, test, or launcher entry point. Start by locating the launcher method and reviewing the related changes in PR #4990, then identify the argument-validation branches and timeout-string construction mentioned here. Done means those pieces are separated into small, testable methods without changing the launcher's behavior.

Written by the indexing model from the issue text.