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

Yes

The word "livraria" has the exact same meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only differences are phonetic. In Brazil, the vowels tend to be more open and the pronunciation is more melodic/syllable-timed. In Portugal, the unstressed vowels are much more "reduced" or closed, and the rhythm is more stress-timed, which can make the word sound shorter or more clipped to a Brazilian ear.

Brazilian Portuguese Examples

1. Eu adoro passar horas em uma livraria. (I love spending hours in a bookstore.)
2. Você sabe se tem alguma livraria aberta agora? (Do you know if there is any bookstore open now?)
3. Comprei esse presente na livraria do shopping. (I bought this gift at the mall bookstore.) Note: Brazilians almost exclusively use "shopping" to refer to a shopping mall.
4. A livraria está fazendo uma promoção de livros. (The bookstore is having a book sale.)
5. Eu estava andando na livraria procurando um clássico. (I was walking around the bookstore looking for a classic.)

Portuguese (Portugal) Examples

1. Adoro passar horas numa livraria. (I love spending hours in a bookstore.)
2. Sabes se há alguma livraria aberta agora? (Do you know if there is any bookstore open now?) Note: A Portuguese person would more naturally use "tu" (implied in "sabes") and "há" instead of "tem".
3. Comprei este presente na livraria do centro comercial. (I bought this gift at the shopping center bookstore.) Note: In Portugal, "centro comercial" is the standard term instead of "shopping".
4. A livraria está a fazer uma promoção de livros. (The bookstore is having a book sale.) Note: Portugal uses the "a + infinitive" construction instead of the Brazilian gerund ("fazendo").
5. Estava a percorrer a livraria à procura de um clássico. (I was walking through the bookstore looking for a classic.)