The Costco version will look for information you saved on your hard drive when you ask to have information transferred from prior year. I assume the online version probably stores files locally but not sure.
If you used the online version last year and need to transfer your info to this year's Desktop version there are 2 ways depending on what you have.
1. If you saved the actual .tax2021 file (not just the pdf file) to your computer before online was shut down in Oct. then start a new return and the very first thing you do is Transfer from .tax file. You can only transfer at the very beginning. You should be able to download the .tax2021 file from Online. See this to download the .tax data file, the second section on how to get the data file from the prior year.
2. If you didn't save the .tax file to your computer or lost it, there is a way to do it by starting a 2022 return in the Online version, transfer to that and then continue in the desktop version. You won't have to pay for Online.
First transfer into the Online version
Then to switch to the Desktop program
Here's how to transfer last year's return to Windows Desktop program
How to transfer into Turbo Tax for Mac