Windows build number: Microsoft Windows [version10.0.18362.175]
Windows Terminal version (if applicable): Version: 0.2.1831.0
Any other software?
Anaconda

use cmd:

# Actual behavior
You're demonstrating with powershell in the "broken" screenshot and cmd in the "working" one. This might just be how conda activate _works_. If it is a .cmd or .bat file that is setting environment variables, it just won't work from PowerShell. We can't change that.
For the benefit of somebody finding this from Google:
Anaconda 4.6.0 and later supports PowerShell by running conda init powershell after the installation. Having done that, Terminal works with Anaconda out of the box.
Most helpful comment
For the benefit of somebody finding this from Google:
Anaconda 4.6.0 and later supports PowerShell by running
conda init powershellafter the installation. Having done that, Terminal works with Anaconda out of the box.