sachakanner Solus supports Snap and Flatpak, both. The Third Party repository is closed and no new applications will be added to that repository, as I understand it. But between Snap and Flatpak, you can find most commonly-used third party apps.
I don't use Snap, so I'm not entirely sure how to install Snap apps up in Solus, but snapd is installed and Draw.io is in the Snap Store. I hope that someone who uses Snaps will be along to help.
I prefer Flatpak. I use Flatpak for Microsoft Edge and for Zoom, and have installed other third-party apps using Flatpak from time to time. Flatpak works well with Solus.
Draw.io is available as a Flatpak if you want to use it as a Flatpak.
To install Draw.io as a flatpak, first run
flatpak remote-add --if-not-exists flathub https://flathub.org/repo/flathub.flatpakrepo
in the terminal, reboot, and then run
flatpak install flathub com.jgraph.drawio.desktop
in the terminal.
Reboot again and Draw.io will show up in the menu.
The drill is identical for other apps in the Flathub, although you only have to install the Flathub repository once, the first time you install a Flatpak. After that, just follow the instructions for the particular app (flatpak install flathub.com <package>).