For the ordinary people, you would not bake with yeast through the week of Passover, correct, but there are different mitzvot regarding the mishkan, and temple, the shewbread or bread of the presence was not baked with leaven, there was to be no unclean thing within the holy place. Unclean, leaven = sin. So these loaves were round and kinda like large pita breads, flat like that, made with no leaven, but not like we are used to seeing with modern day matzah. Modern day matzah is rolled very thin and baked under 18 minutes so yeast doesn't have time to form ( as you don't have to add yeast to dough, it is in the air).
The offerings in the temple were of unleavened bread also, with this exception Feast of first fruits of summer, this is at Shavuot, there was a wave offering of the people of two leavened loaves of bread, that's us, the people, we have sin in us.
Here is an example from Exodus, when the Aaronic priests are being sanctified
1And this is the thing that thou shalt do unto them to hallow them, to minister unto me in the priest's office: Take one young bullock, and two rams without blemish,
2And unleavened bread, and cakes unleavened tempered with oil, and wafers unleavened anointed with oil: of wheaten flour shalt thou make them.
Exo 23:18
Thou shalt not offer the blood of my sacrifice
with leavened bread; neither shall the fat of my sacrifice remain until the morning.
Leviticus:
2:4And if thou bring an oblation of a meat offering baken in the oven, i
t shall be unleavened cakes of fine flour mingled with oil, o
r unleavened wafers anointed with oil.
Also the shewbread was only allowed to be eaten by the priests after it's week was up, they could eat it when the 'new batch' was made and placed upon the table. It had to be eaten standing up also as this was not a meal but a duty of the priests.