I have the exact same problem when trying to install Minnesota State for TurboTax Premier 2023 for Desktop on 12/21/2023. It shows the state as downloaded, but will not apply it to my current tax file. At the top of the screen, I still see "See Amount" line in the state tax section. Clicking on that takes me through the same repetitive process with a window of "Here are the states you've downloaded. Check the box next to each state to add it to your return...". Checking the box beside Minnesota and "Download Now" leads to another prompt "Let's Download and Install Your States" which results in a "Your software is up to date" message and then still the "See Amount" line under the state section.
