While generally speaking, you can simply copy an app bundle from one Mac to another, it doesn't carry over the user data and app preferences that the app generates and stored elsewhere (generally somewhere in users home directory).
Also, not every app Mac installs as a .app bundle and may have installed files elsewhere, causing the copying over .app bundle approach to not work well.
Recommended approaches that you can take are:
Reinstall the apps from source. It could be either Mac App Store, Homebrew Cask or direct download from the publishers website. This way you'd get the apps installed afresh and in the way the developer intended.
Also, even if some of the apps are paid, most Mac apps come with a licenses that lets you use them on all of your personal Macs.
This approach may have a drawback where you may lose app specific preferences and data (not necessarily user data but data such as plug-ins which is directly managed by the app).
However, this approach would be the most likely recommended one as it would let you have a clean install.
If you are concerned about losing app specific configuration and app data, you may consider using Migration Assistance or restoring to the new Mac via a Time Machine backup.
The benefit here would be that you can technically set your new Mac to be in the same state as the old one.
Once you have your new Mac setup, you can then normally uninstall the apps that you don't need, and, get rid of any data that got carried over and is not needed on the new machine.
So to conclude, if the app that you are looking to transfer was installed simply as a .app bundle, has not installed anything outside, and doesn't have any customisations that you care about losing, you'd be safe copying it over. (But then again, what's possibly preventing you from re-installing them from source?)