No, I didn't need to log in. Both STGs likely support WFS 2.
I have ultimately proceeded as follows:
First, I re-read and cleared the fault memory from the old ECU. Then, I removed the old ECU and installed the new one. I turned the ignition on and connected the laptop. Then, I went to WFS (25) in VAG-COM, first cleared the memory and then went to Adapt (10). I read, saved, and confirmed channel 00. Then, I cleared the fault memory in the new ECU and turned off the ignition for about 1 minute. The car then started immediately - so everything was done correctly
Now I'm driving with a fully functional STG and around 140 horsepower.