Why did the eastern tribes say they built a large altar by the Jordan?

Answer: As a witness, not for sacrifices

Reuben, Gad and half of Manasseh said the altar was not for burnt offerings but a witness that they too worshiped the LORD.

“That is why we said, ‘Let us take action and build an altar for ourselves, but not for burnt offerings or sacrifices.”— Joshua 22:26 (BSB)