If you don’t mind me chiming in, I don’t think Padmé being pregnant was really a big secret, and I don’t think her being pregnant and unmarried would’ve been seen as scandalous. What she is worried about is people finding out the father is a Jedi. That would be the scandal. If she had a baby with a normal citizen, the Queen nor the Senate would likely care, beyond general gossip. But being in a romantic relationship with a Jedi is not only against the Jedi code, but it is a clear conflict of interest in regards to the balance of power between the Senate and the Jedi.

As far as Anakin not noticing her baby bump, it is possible that it was just hard to notice through a blurry hologram… Or maybe he just thought she was gaining weight and didn’t want to mention it…