When it comes to the internet, fonts are generally pre-installed and loaded onto Browsers by the OS - Not all phone OS versions are equal, especially Android, and may not have as wide of a selection of fonts as Windows 10 or 11.
Some fonts, usually custom ones can be displayed by the browser alone, these are called "web-fonts". If these are unable to be displayed for whatever reason (Script blockers, Security & Privacy controls, browser limitations) then there's usually a fallback font that is displayed often referred to as "web-safe", one that is widely supported and available on most OS; such as Arial or Georgia.
Outside of custom fonts, any officially licensed font will need to be installed on your OS in order for you to see it. For example if an Android phone does not have Times New Roman installed then it will display them in the system default instead, which is often Roboto (Androids font)
It's most likely that your phone simply doesn't have a wide selection of fonts, most Android OS come pre-installed with only a couple, if even. Usually they'll default to their own Font (Roboto) and allow you to purchase licenses for other fonts from the store. You should be able to find a list of what you have and where to purchase them in your phones Settings.