I am using Monterey 12.5 and am facing this exact same issue with chrome. I can get a copy of the HAR file when I use chrome headless with a HAR extractor javascript code (https://github.com/cyrus-and/chrome-har-capturer) but I am not able to extract the HAR files from the chrome GUI.
I don't know the reason behind it and was curious if this my resolved in any way by the original author @Toonetown