Where can I see how a program was installed?

Start with which zoom or which zoom-client. That will return the file-path to the executable. (Hint: tab completion is your friend)

Anything that starts with /snap was installed by Snap (Or the Ubuntu Software Center) so you can find out more by opening the software center or running snap list | grep -i zoom to get full/correct Snap name.

If it starts with /usr/bin it was probably installed with apt or Synaptic. In that case dpkg -l | grep -i zoom or apt policy zoom* will tell you more. Look at the "Installed (Local or Obsolete)" filter in Synaptic to see whether something installed by apt was local or via a repository.

You may also want to check for:

• Flatpak - check with flatpak list | grep -i zoom
• Ubuntu Make - check with umake --list-installed (For example, IDEs)

Install Synaptic Package Manager (you can install it from Ubuntu Software, or from command line using sudo apt install synaptic). It is a great tool to manage .deb packages. On the main screen, it shows you packages divided into groups, as you can see in the screenshot below. Look at group called "Installed (local or obsolete)" - these are packages that have been installed from manually downloaded files and not from repositories (some very essential system packages, like libc, are also included there). On my screenshot you can see zoom among those packages.

BTW. In your Slack example, the program is installed as snap, not a .deb package, which can be recognized by the presence of "Channel" at the beginning of the data on your screenshot. Snap packages always have a channel (usually latest/stable) while .deb packages don't. So neither apt nor Synaptic won't know anything about that package (in fact, in your example apt policy is showing you information about a non-installed slack package available to install as .deb from the repositories).