Learn Russian: Они не финансируют этот проект, так как он слишком дорогой. - They do not finance this project, as it is too expensive.

You could use the reflexive passive: Этот проект не финансируется (ими). However, in Russian, using an active verb with a subject (Они не финансируют...) is usually more natural in speech. The passive version sounds much more bureaucratic, formal, or academic, which is a key register distinction to keep in mind.

Why use так как instead of потому что for "as" or "because"?

Так как is slightly more formal and structured than the everyday потому что. Using так как here fits the professional context of discussing project financing perfectly, whereas потому что would sound a bit more conversational.

As a refresher, why does the verb финансировать conjugate to финансируют instead of keeping the "ова"?

This is a standard rule for verbs ending in -овать or -евать. In the present and simple future tenses, the -ова- or -ева- suffix drops out and is replaced by -у- or -ю-. Therefore, финансировать becomes финансир- plus the ending -уют.

Could we use the short-form adjective дорог instead of the full-form дорогой?