Is there a program like Fedy but for Ubuntu?

Try the Software-Boutique, which comes default with Ubuntu-MATE, but can be installed & run from any *Ubuntu. If the selected software requires a PPA be added, the Boutique adds it for you.

https://snapcraft.io/software-boutique

It doesn't list every piece of software, trying to limit itself to the 'best' (or top-of-class) for each category.

To install (snap) on my 18.04 laptop, I needed to use

sudo snap install ubuntu-mate-welcome --classic
sudo snap install software-boutique  --classic

and it was run with ubuntu-mate-welcome --boutique

but I suggest giving the snap version a miss if using a limited resource machine, it was painful on this dual core machine with only 2gb ram, I've had no issues using non-snap version