In itch v25, the main log is in $XDG_CONFIG/.config/itch/logs/itch.txt on Linux, %APPDATA%/itch/logs/itch.txt on Windows, ~/Library/Application Support/itch/logs/itch.txt on macOS.
$XDG_CONFIG/.config/itch/logs/itch.txt
%APPDATA%/itch/logs/itch.txt
~/Library/Application Support/itch/logs/itch.txt