No, TurboTax will not share data between two computers, or consolidate data from two different computers. Your tax return data is saved only on the computer that you are working on when you enter the data.
The safest procedure is to just use one computer to prepare your joint tax return. If you want to use two different computers, you must copy the tax return data file from one computer to the other each time you want to switch computers, and make sure you open the correct latest version of the file each time you start TurboTax. You cannot work on both computers simultaneously. The tax return data file for a 2021 tax return has the file name extension .tax2021 and whatever name you give it when you save it.