But all those places were near the Bōdhi tree, at the same site.
– The description there says the Buddha left that site after some time. Does not specify the total time spent in the vicinity of the Bōdhi tree.
Yes, 5 weeks at the site. But it is also not clear if this Bodhi tree is the tree where he attained enlightment.
The text says:
“Soon after his awakening, the Buddha was staying at Uruvelā on the bank of the river Nerañjara at the foot of a Bodhi tree.”