SHA-256 Hash over multiple SHA-256 Hashes
Yes, this is fine for verifying that the file contents match the original. You are basically using a hash list. As long as SHA-256 is collision resistant, there is no way to find a hash that would be ambiguous and refer to two or more known file sets.

In addition to the potential issues mentioned in the comments, storing just the aggregate hash value leaves you with no way to figure out which file failed to match. That is why it is common to store the intermediate hashes as well to see which file would have to be e.g. downloaded again.