I read online that some rabbis say that eating matzah throughout the holiday is commendable and praiseworthy and not just limited to the first two nights when it is obligatory. What is this referring to? Is this only “shmurah” matzoh? Also there are “machine made” square shmurah matzah does it apply to that or only handmade shmurah matzoh. For example see attached.
That is correct. according to the Vilna Gaon, it is a mitzva to eat matzah for all seven (eight) days of Pesach and not just on the first night. Many rishonim however say that although it isn’t a requirement, nevertheless every time one eats matzah during Pesach one fulfilled a mitzva to eat matzah, The idea of Shmura Matzah, (watched Matzoh) is that the matzos eaten on Pesach are to be watched to make sure they don’t become chometz, and made with the intention to use them for the mitzva of eating matzoh on Pesach. Essentially the matzoh has to be watched from the time it is kneaded, however there are opinions that it should be from the time it is harvested. The laws of Shmura matzoh apply to both round (handmade) and to square (machine) matzoh.
Have a chag Kasher V’samech
Pesachim 120a, Rambam Chametz Umatzah 6-1, HIlchos Chag Bchag 16 ftnt. 23, Shulchan Aruch 460-1, 453-4, M:B 460-2,3.