Application data is usually in your home folder.
Application settings are often (not always) in your home folder. Some applications keep settings in live databases (like gsettings) instead of static config files.
Applications are almost never in your home folder. The installed applications are in /bin, /sbin, /usr/bin, /usr/sbin, and many other possible places - mostly owned by root (not you). To sync application versions like that on a Debian system, your should simply be ensuring you keep the same package versions.
Many customizations settings are in your home folder, others may be scattered among gsettings, /etc, environment variables, and other places.
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