Ubuntu uses Gnome Shell as its desktop environment. The dock is created by a Gnome Shell extension, "Ubuntu Dock", which is derived of "Dash to Dock". Neither Gnome Shell nor the extensions support the visual effect of enlarging icons, so as such, the answer is "no". The feature is also not available in the app section.
As it turns out, Gnome decided to change icon naming convention. This was done ~3 years ago. The change not only wasn't documented anywhere, but the old documentation still exist and is promoted, as if it was still actual. Sources:
The only solution ...
Ubuntu 20.04 on Wayland
Press Alt + F2
Type "lg" and hit Enter (Looking Glass)
Click on the "Windows" tab.
You should see the titles of all your windows. Below each one you will find a wmclass property. Write down or copy the value you see.
Open up the .desktop config file corresponding to your application. It should be in the ~/.local/...