In some contexts, a bit can refer to a boolean variable, a flag. In other contexts, it may refer to the voltage at a certain point, or any number of other things. But when you are talking about bits/s then it’s a measure of information.

These are not the same thing because the amount of information contained in a bit is not always equal to one bit of entropy.

Yes, but as you know, this implies that the information is already available. You can use that knowledge to create a compression algorithm, or to define a less redundant file format. That’s very practical.

We can also be a bit philosophical and ask: How much information does a backup contain? The answer could be: By definition, 0 bits. That’s not a useful answer, which implies a problem with the application of the definition.

A more interesting question might be: How much information does a file contain, that stores the first 1 million digits of the number π?