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

No

While the word "participar" shares the core meaning of "to take part" or "to participate" in both variants, the answer is No because there is a significant difference in typical usage and grammar.

In Brazilian Portuguese, "participar" is almost exclusively used to mean "to take part in" (usually requiring the preposition de) or "to share/partake in" (e.g., participar a alegria). In Continental Portuguese, "participar" has a much more common secondary usage: to "notify," "announce," or "inform" (e.g., participar um nascimento). Furthermore, the grammatical regimen (the way it connects to objects) differs; in Portugal, it is frequently used as a transitive direct verb (to notify something), whereas in Brazil, it is used as a transitive indirect verb (to participate in something).

Brazilian Portuguese

1. Eu quero participar do projeto. (I want to participate in the project.)
2. Ele participou da reunião ontem. (He participated in the meeting yesterday.)
3. Nós vamos participar do evento de amanhã. (We are going to participate in tomorrow's event.)
4. Eles participam de todos os jogos do campeonato. (They participate in all the games of the championship.)
5. Venho participar o meu interesse na vaga. (I am [formally] notifying [you] of my interest in the vacancy.)

Continental Portuguese

1. Eu quero participar do projeto. (I want to participate in the project.)
2. Ele participou da reunião ontem. (He participated in the meeting yesterday.)
3. Nós vamos participar do evento de amanhã. (We are going to participate in tomorrow's event.)
4. Eles participam de todos os jogos do campeonato. (They participate in all the games of the championship.)
5. Venho participar-lhe do meu interesse na vaga. (I am notifying you of my interest in the vacancy.)