However, since the update, my profiles are not loading correctly when I load an aircraft in MSFS 2020.
There has been no change at all in how profiles are handled in this version. What do you mean by 'mot loading correctly'? The name of the currently loaded profile is shown in the FSUIPC7 main window - do you see the profile name there?
Regarding the in-game control settings in MSFS 2020: how should they be configured when using FSUIPC profiles? Should I leave them as "Default" or should I clear/unassign the bindings in the simulator to avoid conflicts?
It is up to you. If assigning a button/switch/axis in FSUIPC, you should certainly remove any assignments to the same button/switch/axis from MSFS. If assigning everything in FSUIPC, better to start with empty assignments in MSFS, although it is perfectly fine to have some assignments in MSFS and others in FSUIPC.
What files do you need from me to help investigate this issue? I assume you need my FSUIPC7.log and FSUIPC7.ini files. (I have attached them to this post just in case).
Just the log and ini files. You may need some additional logging set, depending on your issue. Looks like you have attached the same log file several times, and it has a lot of logging set. If you have a problem with a profile-specific button assignment not working, just set logging for Buttons & Switches and show me a log file where you attempt to trigger the assignment. Turn off other logging as it will just fill the log with unneeded inofrmation.