TREATY? What treaty?
There was a simple joint resolution by the US congress spelling out what Texas had to do to be considered for admission to the Union. There was an ordinance as required by the Joint Resolution, passed by the Texas legislature agreeing to do all of those things which included a requirement that the people of Texas vote on admission as Congress required, followed by a vote (90% + approving) and then followed by an ACT of Congress officially admitting Texas as a state.
They were two Congressional actions by both houses of Congress but no treaties of any kind. Here is a link to all of the relevant documents.
You will notice that there is nothing in any of them about the Federal Government having to "purchase" land. In fact, they specifically require Texas to give deed to the United States all armories, forts and military stores required for the common defense. And there is absolutely nothing in the documents giving Texas any sort of "right" to secede at will.
Read the post regarding what the Republic of Texas required.
The United States and The Republic of Texas were negotiating as equals.