Learn Russian: Вчера мы реализовали этот успешный проект. - Yesterday we implemented this successful project.

Biaspectual verbs have only one form for both imperfective and perfective aspects. To resolve the aspect, we rely on context. Here, the time marker Вчера combined with a single, completed result (a successful project) strongly points to the perfective aspect. We accomplished the goal.

If I wanted to say we were in the process of implementing it yesterday, would the sentence change?

The verb реализовали would actually stay exactly the same! Because it is biaspectual, it can also act as an imperfective verb. To force that meaning, you would change the context by adding a duration marker, such as Вчера мы весь день реализовали этот проект (Yesterday we spent all day implementing this project).

Are most biaspectual verbs borrowed words like реализовать?

Yes, a large number of biaspectual verbs in Russian are foreign loanwords that end in -овать or -ировать. Other common examples you will see at this level include организовать (to organize), использовать (to use), and арестовать (to arrest).

Why does the direct object этот успешный проект look like it is in the nominative case?

It is actually in the accusative case. For masculine inanimate nouns like проект, the accusative form is identical to the nominative. The demonstrative pronoun этот and the adjective успешный also take this inanimate accusative form, which perfectly mirrors the nominative.