Yeah, I know about it and I've read the law, but as you say, they're still developing it and it hasn't been put into practice yet. It's a pity, but at least they have passed the law and we can expect it to be applied sometime in the near future!
About what you say, the problem is that the change of the "legal sex" and name is a competence of the Civil Register, which depends on the Ministry of Justice and, therefore, on the Central Government, so you'll need to follow the process of the 2007 Law (Ley 3/2007, de 15 de marzo, reguladora de la rectificación registral de la mención relativa al sexo de las personas,
https://boe.es/buscar/doc.php?id=BOE-A-2007-5585) and all the requisites of art. 4 (including the one of the 2 years). No regional Law can affect this process (maybe yes if there is some kind of local ID, what do you mean with it?), so Regional Governments only can offer free services to help you, but not too more.
I'm sorry I can't help more, that's the Law now. Nonetheless, there is movement in the Congress to propose (and probably pass) an integral trans Law during this year.
PD: if you don't understand something please tell me, I'm not used to explaining this sort of legal stuff in English and I may have committed some errors.