Hi
Please don’t purchase Minecraft again yet.
First sign in at https://www.minecraft.net/en-us/msaprofile with the Microsoft account you migrated to, then check “My Games.” If Minecraft appears there, the license is still attached to that account.
If it is listed as owned, sign out of the Minecraft Launcher, Xbox app, and Microsoft Store, then sign back into all three with that exact same Microsoft account. A Store/Xbox account mismatch is a common reason the Launcher shows “Buy” instead of “Play.”
Then download the current Launcher from https://www.minecraft.net/en-us/download and try again.
If “My Games” itself shows “Buy Now,” the issue is with which Microsoft account holds the migrated license rather than the Launcher installation.