It's not an app so it won't show up there, you should be able to install it manually in the command prompt with:
sudo apt install android-sdk-platform-tools-common package
But that's unlikely to let you proceed with the installation without hiccups since your browser is still a flatpak. Do you have another Android phone in reach by any chance? If it's relatively modern it's likely you can use that as the host device. Simply open the web installer there and connect that phone with your pixel.