In the sentence "nada ha cambiado", the verb cambiar is intransitive (i.e., it has no direct object). Looking at the definitions of cambiar on DLE, the definition that fits is:
- intr. Modificarse la apariencia, condición o comportamiento. Ha cambiado el viento, el tiempo.
which is not listed as pronominal ("prnl."), so cambiarse is not used to refer to things that change (though, according to definition 7, it seems to be possible to use cambiarse for persons that change). The correct sentence is therefore the first one:
- Estoy tan feliz ahora como cuando éramos ricos y teníamos todo lo que queríamos. Créame, al menos para mí, nada ha cambiado.
Note also that comparisons of equality in Spanish are expressed using "tan + adj. + como", and not "tan + adj. + que". I also fixed this in the sentence.
The phrase "nada se cambió" could appear in sentences where "nada" is the direct object, and "se" is reflexive passive. In this case, it would mean "nothing was changed":
- Se discutió mucho sobre la necesidad de modernizar los procesos de fabricación, pero al final nada se cambió (The need for modernization of the manufacturing processes was discussed a lot, but in the end nothing was changed).
This phrase ("nada se cambió") implies that there is an agent that could have changed something, but they did not change anything. This idea can also be expressed as "no se cambió nada". This does not apply to your example sentences, where "nada" is the subject.