That is odd that it is not in the Software Store here but is in the Ubuntu mate store.
I think it is likely you will need to use the terminal. Though, personally, I recommend using the terminal for all installs, as much as possible. It allows you to watch what is going on, see any troubles that come up and know what is being installed. The only difference between using the terminal and using the Software Store is that the terminal gives you far greater control.
If doing from terminal, I suggest avoiding the Snap Install.
The Snap Install looks simpler. Must be very appealing to Windows users. But it is plagued with problems and you would be better off with something that updates from source.
Sadly… it requires pasting in Three commands instead of One command.
When will the suffering end?
curl -s https://brave-browser-apt-release.s3.brave.com/brave-core.asc | sudo apt-key --keyring /etc/apt/trusted.gpg.d/brave-browser-release.gpg add -
sudo sh -c ‘echo “deb [arch=amd64] https://brave-browser-apt-release.s3.brave.com
lsb_release -sc main” >> /etc/apt/sources.list.d/brave.list’
sudo apt update && install brave-browser brave-keyring