I can’t transfer anyone.
I haven’t been playing the classic since BC, come back and I have a couple toons on Sulfuras which apparently is a “locked” and dead server. I have no option to transfer, but thought i read somewhere, there would be.
In the meantime, I started a character, leveled to level 15 and paid to transfer to another server. The service is “grayed” out. I have several other toons and none of them have an option to be transferred.
EDIT: I found the option to transfer for free off Sulfuras. Still can’t transfer anyone else from a normal realm though