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

Yes

The spelling, meaning, and grammatical function of "sirvo" are identical in both Brazilian and Continental Portuguese. It is the first-person singular present indicative of the verb servir (to serve). The only differences are found in pronunciation: Brazilian Portuguese generally features more open vowels and a different articulation of the "r," while Continental Portuguese is characterized by significant vowel reduction (making unstressed vowels sound almost silent) and a more closed phonetic rhythm.

Brazilian Portuguese Examples

1. Eu sirvo o café para os meus amigos. (I serve coffee to my friends.)
2. Eu sirvo o jantar para a minha família. (I serve dinner to my family.)
3. Eu sirvo como voluntário na ONG. (I serve as a volunteer at the NGO.)
4. Eu sirvo apenas para o que for necessário. (I serve only for whatever is necessary.)
5. Eu sirvo a mesa quando chega a hora. (I set the table when the time comes.)

Continental Portuguese Examples

1. Eu sirvo o café aos meus amigos. (I serve coffee to my friends.)
2. Eu sirvo o jantar à minha família. (I serve dinner to my family.)
3. Eu sirvo como voluntário na ONG. (I serve as a volunteer at the NGO.)
4. Eu sirvo apenas para o que for necessário. (I serve only for whatever is necessary.)
5. Eu sirvo a mesa quando chega a hora. (I set the table when the time comes.)