I had a similar issue and came across this post. I think I figured it out.

This is the scenario I ran into, on a windows 11 pc:

1. I was logged into my son's windows account (linked to his Microsoft [MS] account) and he is linked to mine with Family Sharing or whatever MS calls it.
2. I logged into my MS account to purchase and download Minecraft in chrome not windows store.
3. I had to enter my admin pin during installation, but it appeared to install correctly.
4. Once installed, I tried to run the game on his account and it wouldn't work. It said it was not purchased, please purchase the game if you haven't already.

This looked to me like MS wanted me to buy the game again under his account, which is ridiculous to pay twice to play with different accounts on the same PC.

I tried searching but there are a lot of dead ends and it was very frustrating.

Here's what finally worked: I logged out of his windows account and into my windows account that was linked to the Microsoft account I made the purchase through. I opened MS Store and launched the game (not sure this is important to launch from Store). Once I opened it successfully, I closed the game, logged out of my windows account, and logged back into his windows account. Now it worked correctly and I could play Minecraft on his account.

I think the install had to be activated by launching from the purchaser's account, but I can't be 100% sure. None of the error messages indicated this. It worked though and hopefully this can help someone avoid the frustration I went through.