I don't think the Bible says which way the walls fell. Archaeology found mud bricks at the bottom of the mound on which the walls were built and so that suggests outwards.
One section of the wall did not fall according to archaeology and that would be where Rahab lived in the wall.
The site that says there were no walls (and probably no Jericho) at the time of the supposed Israelite conquest would be the archaeologists that give a late date for the conquest (about 1200BC) and not the Biblical date of (about 1400BC), and so end up saying that there was no conquest of Canaan by Israel. They end up making up other scenarios for how the Israelites came to be in Canaan, and say the conquest did not happen.
There are no Israelite conquest or invasion of Canaan in either dates of c 1400 BCE or c 1200 BCE, because of Egyptian presence in Canaan and Syria.
According to 1 Kings 6:1, the “exodus” took place at Rameses (Exodus 12:37) about 480 years before Solomon’s 4th year, which would mean 1447 BCE be the date of exodus, and Moses’ death and Joshua’s leadership in 1407 BCE.
If this was true, then the Israelites would have cross the Jordan either 1407 or 1406 BC, meaning the battle of Jericho.
The problem here, Canaan was it would have occurred in the reign of Amenhotep II (1427 - 1401 BCE).
Like his father, Thutmose III (1479 - 1425 BCE), they both battled with the Mitanni empire, a kingdom in northeast Syria for southwest Syria and Canaan.
Amenhotep’s son, Thutmose III (1401 - 1391 BCE) found more diplomatic relations with Mitanni, by marrying Mitanni princess, hence retaining control over Canaan.
So the biblical date for Jericho couldn’t have happened in the late 15th century BCE.
As to around the late 13th century BCE, Canaan was under Egypt’s control during the reigns of Ramesses II (1279 - 1213 BCE) , Merneptah (1213 - 1203 BCE) and Seti II (1203 - 1197 BCE).
We know that the Israelites didn’t conquered Canaan, because in Merneptah’s reign, because the famous Merneptah Stele recorded the string of victories against Libya, and much shorter description of his victories against Syria and Canaan, and one line that stated Israel was laid waste.
Plus, the abandonment of Jericho occurred about 1570 BCE, including the destruction of walls. That’s about 160 years before the biblical narrative of Jericho (c 1406 BCE).
Note that the biblical city of Rameses, is actually named Pi-Ramesses in Egyptian (meaning house of Ramesses), which only started construction in the reign of Seti, in honour of his father Ramesses I, but Ramesses wasn’t completed till the reign of Ramesses II.
So Jericho destruction (c 1570 BCE) occurred almost 300 before Pi-Ramesses was completed in 1250 BCE, whereas Exodus and Joshua have the timeline the other way around, Rameses first, then Jericho later.
I don’t think Moses and Joshua exist in any case, so the question of Jericho and Rameses are wrong, historically and archaeologically.