No, you do not need to install one eSIM profile per country, nor do you need to install multiple eSIM profiles at the same time. You only need to install one eSIM profile on your device for all your travels.
Indeed, a single Ubigi eSIM profile installed on your device will allow you to connect in all countries.
After installing your Ubigi eSIM profile, simply log in to your Ubigi account via the app, choose the data plan corresponding to the country you are traveling to, complete your purchase and enjoy your connection!