I'm sorry, I'm not directly answering your question ("Why didn't they mention Data?"). I couldn't find any production notes, and I couldn't reach the story author (Brannon Braga) or the director (David Livingston).

But - I do have a decent in-universe explanation of why Data's story didn't matter.

Data was a unique being that Starfleet discovered, consisting of hardware that had yet to be reproduced. This ultimately led to him being granted the full legal status of "person".

The Doctor was pure software, and was entirely designed and programmed by Starfleet. Even after litigation, he still wasn't granted the status of "person". He was only granted the "economic" status of "Artist", which gave him the right to control his holonovel.

Pulled from Memory Alpha (the Star Trek wiki):

While it had been determined that Data, although being a machine, was not Starfleet property and thus had the right to choose what to do with his life (and thus could most likely be considered a person), it seems the whole process had to be repeated for The Doctor and fellow holograms. The situation here is even more complex than with Data, since Data was a unique single being who was not created by Starfleet (he was found by Starfleet personnel), while holograms were programmed and designed by Starfleet and integrated into ships, space stations and other Starfleet property. In the end, it is not acknowledged in this episode that The Doctor is a person, but he is rather granted the status of an artist.

I'm sorry, I'm not directly answering your question ("Why didn't they mention Data?"). I couldn't find any production notes, and I couldn't reach the story author (Brannon Braga) or the director (David Livingston).

But - I do have a decent in-universe explanation of why Data's story didn't matter.

Data was a unique being that Starfleet discovered, consisting of hardware that had yet to be reproduced. This ultimately led to him being granted the full legal status of "person".

The Doctor was pure software, and was entirely designed and programmed by Starfleet. Even after litigation, he still wasn't granted the status of "person". He was only granted the "economic" status of "Artist", which gave him the right to control his holonovel.

Pulled from Memory Alpha (the Star Trek wiki):

While it had been determined that Data, although being a machine, was not Starfleet property and thus had the right to choose what to do with his life (and thus could most likely be considered a person), it seems the whole process had to be repeated for The Doctor and fellow holograms. The situation here is even more complex than with Data, since Data was a unique single being who was not created by Starfleet (he was found by Starfleet personnel), while holograms were programmed and designed by Starfleet and integrated into ships, space stations and other Starfleet property. In the end, it is not acknowledged in this episode that The Doctor is a person, but he is rather granted the status of an artist.