std/var - streamline code and improve edge cases handling

[NRJank]

• improve performance of var and std by streamlining input checks, reducing repeated function calls, and structuring condition checks to reduce overhead.
• replace expensive calls to cast, repmat, and shiftdim with alternative vector replication calls.
• improve handling of matrix and vector inputs and weights.
• ensure single class preservation in shortcut paths.
• update docstrings to match expected behavior.
• use variable names matching docstring names.
• add tests as needed for items above.
• NOTE: did not streamline redundant tests from statistics and core.