This is a big topic so I will only give some quick notes. The tablets were made by human hands, of stone from the earth, but were written on by the finger of God in heaven. Jesus’ body, like the stone, was of earthly origin (from His mother Mary) while His message and being (the Word of God) were of heavenly origin.
The tablets were stored in the tent of meeting set up before the ark of the covenant was made when the tablets were brought down from the mountain. Tent of meeting was set up outside the camp immediately upon the tablets being brought down to earth. Joshua (translated Jesus in the LXX) Moses’ assistant who came down from heaven by coming down the mountain, never left the tent (Ex 33:7-11). The tablets remained in the tent of meeting for 8.5 months (time from conception until birth) until the ark of the covenant and the tabernacle were set up and dedicated in the first month of the second year of the Exodus. Joshua of the tribe of Ephraim would have to leave at that time because he was not a priest and was not allowed in the tabernacle. The tent of meeting represented Mary pregnant with Joshua/Jesus the Word of God the ark of the covenant represents Mary not pregnant. The travels and times of the Ark of the Covenant represent the times and travels of Mary. For example the Ark remained in foreign lands for 7 months, I believe represent the 7 months the holy family remained out side of Israel, passing through the philistine territory on the way to and from Egypt.
I believe the other two items the manna and staff were not “in” the ark of the covenant but “before” the ark, because that is where the scripture says they were and because they would probably not fit inside.
The manna was stored in a golden vessel called an omer for it size because the size was such that it would hold the amount of grain from a sheaf of grain. The grain and manna were both unleavened, representing without sin, because leaven represents sin. The Eucharist in the Roman Catholic Church is always unleavened depicting Jesus as without sin. This manna was collected long before the ark was built, I believe it also was placed in the tent of meeting. Manna clearly depicts the bread of life from heaven, but was not the true Bread of Life. Jesus is the true Bread of Life.
The rod of Aaron that budded at least partially represented the Cross of Christ.
The rod that budded was before the rod that swallowed the serpents (Ex 7:12) that turned the Nile to blood, etc. And as a almond rod that bloomed and fruited it represents the tree of life, but Jesus’ cross is the true tree of life and Jesus is the Fruit on that tree.
I think you should also ask:
Why the crown on the ark of the covenant?
Why the 4 rings/seals on the 4 corners?
Why the two golden poles attached to the seal rings?
Grace and peace,