Linux is designed as a multi-user operating system. That means that applications are NOT installed within a single User's /home dir by system applications like apt or snap. It also means that some executables, libraries, services, lockfiles, and others are all stored in standard locations.
This is, of course, very different from the way Windows (which is designed as a single-user OS).
.application dir (or file) in your /home/Your_User dir contains only your own profile and data, of course. Not the application itself, not system-level settings, etc. Note that uninstalling the application WON'T remove this data - you must trash it yourself.
If you installed a deb package using apt, use the command
dpkg -L <package_name> to see exactly what got installed where.
If you installed a snap package using snapd, then the application is in /opt.
The Software Center installed both debs and snaps - only you can determine which you installed.