I have a new idea for why we have 3 Matzos at the Seder. Are you aware of the problem with the Bahag and other earlier sources (the CHILUKIM) that used two matzos (like the RAMBAM and the RIF) when Yom Tov fell on a weekday, but used 3 Matzos when Pesach fell on Shabbos? Why should there be such a distinction?
I suppose the half-Matzah can only be used as part of Lechem Mishnah when fulfilling the requirement of "Lechem Oni," which includes a half-Matzah. For Shabbos, Lechem Oni is not enough. Doesn't the Gra make such a comment in Shulchan Aruch?
Be well, Mordecai
I haven't seen the Gra but I will look it up today. If Lechem Oni can enable a half-Mataza to fullfill the requirement of Lechem Mishna for Yom Tov, why should it not work for Shabbos as well?
The Mitzvah of this Yom Tov evening is to eat Lechem Oni, because it is Pesach. This is not the Mitzvah of Shabbos.
I suppose one can argue that this would run into the discussion of the Ohr Same'ach as to why we do not make Kidush on Yom Kipur she'Chal b'Shabbos, and drink less than a m'Lo Lugmav (if Chatzi Shiur is mid'Rabanan). He proposes that although the normal Mitzvah of Shabbos is Oneg, on this Shabbos, the Mitzvah of the day is to fast since Yom Kipur affects the aspect of Shabbos as well. If so, maybe you can argue that today the "Shabbos" requires Lechem Oni as well.
However, I see a difference between the two. Lechem Oni is not a Mitzvah inherent in the day in general, but it is a specific Mitzvah that is performed this evening alone. In addition, it is not a Halachah pertaining to the type of eating in general that one does today (as the Halachah of not eating Chametz), but rather a specific food that must be eaten once during this evening.
Enjoy your "Lechem Oni!" Best wishes,