Is the word vegana the same in Brazilian and European Portuguese?

Yes

The word "vegana" is identical in Brazilian and Continental Portuguese regarding its meaning, spelling, and grammatical function. The only difference is in pronunciation. In Brazil, the vowels are generally more open and subject to different reductions, whereas in Portugal, the vowels are typically more closed and the pronunciation follows a more phonetic, syllable-timed rhythm.

Brazilian Portuguese Examples

1. Ela é vegana há cinco anos. (She has been vegan for five years.)
2. Minha irmã adotou uma dieta vegana. (My sister adopted a vegan diet.)
3. Tem alguma opção vegana no cardápio? (Is there any vegan option on the menu?)
4. Ela comprou uma bolsa vegana muito bonita. (She bought a very beautiful vegan bag.)
5. Eu achei esse hambúrguer vegano muito legal. (I thought this vegan burger was very cool.)

Continental Portuguese Examples

1. Ela é vegana há cinco anos. (She has been vegan for five years.)
2. A minha irmã adotou uma dieta vegana. (My sister adopted a vegan diet.)
3. Há alguma opção vegana no menu? (Is there any vegan option on the menu?)
4. Ela comprou uma mala vegana muito bonita. (She bought a very beautiful vegan bag.)
5. Eu achei esse hambúrguer vegano muito fixe. (I thought this vegan burger was very cool.)