does copying a copy reduce quality?

Once it is in digital format, the number of copies of that file has no impact. Each file is an exact replication.

Now if you make something of that file, such as printed picture, and then copy that, you are back to a loss of fidelity.

While not as significant as the analog version, there is a potential for degradation from each generation of copy to the next generation copy.

All digital media has an allowance for lost bits and error recovery.
"IF" you lose enough bits in the same data area, a copy or section of a copy could become unrecoverable.

Unless you have a particularly bad reader, I would not expect any bit lose errors to show up before the 16th generation copy.
Realistically, I would expect an average of around 128 generations before bit lose adds up to a data lose.

Chas