Barcelona is lucky to sign him for free. Aubameyang was a great striker in Dortmund, he just did a mistake to choose Arsenal as his next journey. If he moved to Bayern or Real Madrid or Barcelona previously, he may have a different story. His value dropped significantly in Arsenal because he has a personal problem with Arsenal management, not sure what the problem is.
After many failed expensive transfers for Coutinho, Dembele, Griezman and some for defense system, finally Barcelona get a successful transfer for their attacking system, from free transfer. It is their first after many free or very cheap transfers of their star players to other clubs, Messi, Coutinho, Griezman, Suarez.
Aubameyang is no long young but with his good pace, he is still useful and he is not too vulnerable to injuries. Barcelona can expect more from him and if Aubameyang can combine well with Memphis Depay, it will be great for them. They together with Dani Alves will be leaders in a young ambitious team with Gavi, Gabi, Fati, etc.
But for me, Arsenal management is stupid to waste the quality of a top striker like Aubameyang just because of uncertain problems. Well, Barcelona is very happy to have him on their squad now. Considering his performance in the last match, he is likely to shine again.
Arsenal made mistakes to sign a new contract with too high salary for Aubameyang. Previous seasons, they relied on him to have goals and points but after that contract, his contribution dropped a lot and he fell into conflict with coach then club. So Arsenal have to let him go. It's not a happy ending at least for Arsenal.