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

Yes

The only difference between the word in Brazilian Portuguese and Continental Portuguese is pronunciation. In Brazil, the vowels are generally pronounced more openly and clearly. In Portugal, unstressed vowels tend to be reduced or "closed," which can make the word sound more compressed or clipped. The meaning, spelling, and grammar are identical in both variants.

Brazilian Portuguese Examples

1. A primavera é a minha estação favorita. (Spring is my favorite season.)
2. As flores da primavera estão lindas. (The spring flowers are beautiful.)
3. O clima de primavera é muito agradável. (The spring weather is very pleasant.)
4. Ela ainda está na sua primavera. (She is still in her springtime/youth.)
5. A primavera chegou com muita chuva. (Spring arrived with a lot of rain.)

Continental Portuguese Examples

1. A primavera é a minha estação preferida. (Spring is my preferred season.)
2. As flores de primavera são muito belas. (The spring flowers are very beautiful.)
3. O tempo de primavera é muito agradável. (The spring weather is very pleasant.)
4. Sinto o aroma da primavera no ar. (I smell the aroma of spring in the air.)
5. Durante a primavera, os dias tornam-se mais longos. (During spring, the days become longer.)