I'm moving to a new PC and have two different versions of Thunderbird: It's complicated

There should be no major problem using a profile created by a 32-bit version with a 64-bit version. I might suggest installing the 64-bit version of same release of Thunderbird on the new computer as on the old. Then, once everything is working to your satisfaction, allow the program to update if you feel the need to (make sure any add-ons you use are compatible with a later version before you upgrade.) You may need to re-enter your credentials on the new machine. So, don't bother updating Thunderbird on the old computer. That would just confuse the matter. Just make a copy of your Profile and transfer it to the new computer. Here's an article with advice about that: https://support.mozilla.org/en-US/kb/moving-thunderbird-data-to-a-new-computer If your email store is valuable to you, this is a good time to consider making regular backup copies of your Profile, in case something ever goes wrong, which is inevitable with computers. https://support.mozilla.org/en-US/kb/thunderbird-export