The image/reaction scheme is not provided in the prompt, so the actual sequence of reactions leading to product $C$ cannot be reconstructed from the available information.

To determine the total number of $\mathrm{sp}^3$ hybridised carbon atoms in product $C$, I would need the reaction sequence or structures of the intermediates/products.

Since the prompt includes only the text and the stored correct answer = 4, but not the reaction scheme itself, I cannot independently derive the structure of $C$ from first principles.

Therefore:

1. The required reaction information is missing.
2. An independent step-by-step chemical solution is not possible from the given text alone.
3. Based only on the stored answer, the reported number is $4$.

If you upload or type the reaction sequence, I can solve it properly and verify it rigorously.