Prince נָשִׂיא nâsîyʼ, naw-see'; or נָשִׂא nâsiʼ; from
H5375; properly, an exalted one, i.e. a king or sheik; also a rising mist:—captain, chief, cloud, governor, prince, ruler, vapour.
Whoever is the ruler of Israel should be considered "the prince". who could enter the eastern porch and eat bread before the Lord there, I don't think the wording implies that the prince could enter the temple precincts through that porch. If the temple had been built and Jesus had come to that temple instead of the Hasmonean and Herodian temple, then as the king of Israel, Jesus would have been entitled to enter into porch of the east gate and eat bread before the Lord there.
Here's a video by some fellow who has created a model of the Ezekieline temple.
He says Ezekiel's design is too big to fit on the extant mountain. He suggests the area will be extended when the Mount of Olives splits in two. But maybe, had the Jews begun by faith to build according to Ezekiel's design, as the priests began to cross the Red Sea while the waters were still in place, perhaps God would have divided the mountain and extended the area for them, as He divided the waters of the Red Sea for the Israelites to cross over dry shod.
Ezekiel seems to be enjoining the Jews to whom he was showing the temple plans, that they should carry out construction and serve God in it.
Ez. 43:9 Now let them put away their whoredom, and the carcases of their kings, far from me, and I will dwell in the midst of them for ever.
10 Thou son of man, shew the house to the house of Israel, that they may be ashamed of their iniquities: and let them measure the pattern.
11 And if they be ashamed of all that they have done, shew them the form of the house and the fashion thereof, and the goings out thereof and the comings in thereof and all the forms thereof, and all the ordinances thereof and all the forms thereof, and all the laws thereof: and write it in their sight, that they may keep the whole form thereof and all the ordinances thereof and do them.