Learn Spanish (Latin America): Sin embargo, el proyecto es muy próspero.

Even though the prosperity might feel like a current state or phase, próspero (prosperous or thriving) is treated as a defining characteristic of the project. In Spanish, we use ser with adjectives that define the core nature, identity, or inherent qualities of a subject, rather than a temporary physical or emotional condition.

Could I use exitoso instead of próspero here?

Yes, exitoso (successful) is a very common alternative and works perfectly. However, próspero carries a more specific nuance of financial success, ongoing economic growth, or thriving over time (like a booming business), whereas exitoso simply means it achieved its goals.

How would I use this sentence as the 'present result' in a mixed conditional sentence for this lesson?

To say 'If we had not done X, the project would not be very prosperous,' you use the past perfect subjunctive for the past condition and the conditional simple for the present result. For example: Si no hubiéramos invertido, el proyecto no sería tan próspero (If we had not invested, the project would not be so prosperous).

Does sin embargo always have to go at the beginning of the sentence?