I read that the reason the model was pulled from the ready room set was so it could be used as a reference for Jein's team to construct the Stargazer filming model. In one scene, Levar Burton does say "Constitution" class, so they were planning on using the movie model, but couldn't get it or something, so they decided to build the model based on the kitbash, and then dub over that line with "Constellation".
Yeah, what I think happened was this (and someone more in the know can correct me if I'm wrong): They did indeed pull the model so that Jein could use it as a reference. However, during filming of the episode it was determined that Jein wouldn't have the filming model done in time for the post-production VFX, so they filmed the ep with the intention that the Stargazer would be a reuse of the TMP Enterprise (the TMP desktop model, Geordi saying "Constitution class," etc.). But Jein did have his model ready by post, so they went back and dubbed over Geordi's line before the ep was broadcast, and in subsequent episodes the yellow desktop model was returned to the ready room.
The Stargazer was designed by Andrew Probert and Rick Sternbach. The miniature was built by Greg Jein.
The Stargazer was original going be Constitution class, which was seen in Picard ready room in early broadcast episodes that had air before the Battle. But After the episode was film, they decided to not have the Stargazer be a Constitution, but instead a Constellation, which sounded almost the same.
Later on while they were working on the series so it can be release on VHS they went back and edit the early episode, but left the battle episode along. Giving the illusion that they weren't in Picard ready room, but instead was in Commander Riker office and that the Constellation model was in Picard ready room all the time.
What you see airing now days. Are the edit version, not the original air broadcast episodes. Those original air broadcast were either shelve or destroyed?
NCC-7100 was going to be the Stargazer registry number, which was on the model that was in Picard ready room. Later on it was decided that the Stargazer should have a lower registry number, which went on the filming model.