How to install app from older Ubuntu repository on a new Ubuntu

There are two cases:

Installing a Snap package

If the application is found on apps.ubuntu.com, now renamed to snapcraft.io, then it's a "Snap" package that is independent of the version of Ubuntu you want to install it on. You can install it with the "Ubuntu-Software" application on Ubuntu 16.04 and later. Or alternatively from the command line as follows:

sudo snap install pycharm-community --classic

Snap packages are not real software packages, as they come with a redundant version of all kinds of dependencies, which makes them much larger. Also each Snap package uses its own ugly /var/lib/snapd/snaps/… mountpoint, which will show up when listing mounted file systems with mount, for example. So whenever a package is also available as a normal Ubuntu .deb package, better proceed to the next option:

Installing a .deb package from an earlier release

If the application is found with a search on packages.ubuntu.com, it's a real Ubuntu .deb package. To install it in a distribution where it is not (yet) available, go to the package's page in the latest distribution where it is available (random example). Scroll down to the "Download [packagename]" table and click on the correct link in the "Architecture" column, which is usually the amd64 one. Save the file, and then install it in the command line as follows:

sudo apt update
sudo apt upgrade
sudo apt install ./packagename_[version]_amd64.deb

This will automatically install all dependencies as long as they are available in your own release of Ubuntu, which is often the case. The ./ in the command above, or a full path to the file, is important because otherwise apt would look for the package in the repository, where it's not found for your release in this case.

(As for Sweeper 3D, it seems the package was simply pulled from the Snap repository, perhaps by the author himself. It is no longer available for any Ubuntu distribution.)