The Unicode Consortium say:
For compatibility purposes, a few Greek letters are separately encoded as symbols in other character blocks. Examples include U+00B5 μ in the Latin-1 Supplement character block and U+2126 Ω in the Letterlike Symbols character block. The ohm sign is canonically equivalent to the capital omega, and normalization would remove any distinction. Its use is therefore discouraged in favor of capital omega. The same equivalence does not exist between micro sign and mu, and use of either character as micro sign is com- mon; for Greek text, only the mu should be used.
which I think is saying “Don’t use U+2126 Ω (or \ohm in Julia) - use U+0309 (\Omega in Julia)”.