How to update software installed via .deb file

While it can be that installing a program with the .deb package doesn't add the repository to apt for automatic updates, some .deb installations do just that: they add repositories to apt for further updates or make it possible for you to add them manually and then install the software. Example: 'Visual Studio Code'. https://code.visualstudio.com/docs/setup/linux

I cite from their website:

Debian and Ubuntu based distributions

The easiest way to install Visual Studio Code for Debian/Ubuntu based distributions is to download and install the .deb package (64-bit), either through the graphical software center if it's available, or through the command line with:

sudo apt install ./<file>.deb

Installing the .deb package will automatically install the apt repository and signing key to enable auto-updating using the system's package manager. Note that 32-bit and .tar.gz binaries are also available on the VS Code download page.

The repository and key can also be installed manually with the following script:

curl https://packages.microsoft.com/keys/microsoft.asc | gpg --dearmor > packages.microsoft.gpg 
sudo install -o root -g root -m 644 packages.microsoft.gpg /usr/share/keyrings/ 
sudo sh -c 'echo "deb [arch=amd64 signed-by=/usr/share/keyrings/packages.microsoft.gpg] https://packages.microsoft.com/repos/vscode stable main" > /etc/apt/sources.list.d/vscode.list'

Then update the package cache and install the package using:

sudo apt-get install apt-transport-https 
sudo apt-get update 
sudo apt-get install code # or code-insiders

Download a newer .deb and install it just like you installed the previous one.

No, you cannot get automatic updates as part of the normal apt update && apt upgrade process; that's what repositories are for.