Learn Italian: L'ombrello era così bagnato che ha inzuppato il pavimento. - The umbrella was so wet that it soaked the floor.

Yes, absolutely! You can say L'ombrello era talmente bagnato che... without changing the meaning at all. Così ... che and talmente ... che both express a consequence (so ... that) and are completely interchangeable when emphasizing an adjective like bagnato.

Why does the first part use the imperfetto (era) but the second part uses the passato prossimo (ha inzuppato)?

This is a classic example of mixing past tenses to contrast a background state with a completed action. Era così bagnato uses the imperfetto because it describes the ongoing condition of the umbrella. Ha inzuppato il pavimento uses the passato prossimo because soaking the floor is the specific, completed event that happened as a result of that condition.

Since this is a complex sentence with che, why doesn't ha inzuppato use the subjunctive?

Clauses showing a result with così ... che or talmente ... che take the indicative mood when they state a factual, realized outcome. Since the umbrella actually did soak the floor, you use the standard indicative (ha inzuppato). You would generally only see the subjunctive here if the result was just hypothesized, or if the main clause was negative.

What is the difference between bagnato and inzuppato?