Try Azurah: https://www.esoui.com/downloads/info602-Azurah-InterfaceEnhanced.html
I haven't used it for this myself but it lets you move and resize different elements of the UI and the dialogue window is one of the options. I've used it to make various UI elements smaller and that works well, including for text, I assume it will work just as well for making them bigger.
No there does not exist any way to just change the font there.
You culd try if this addon helps (if you aren't already playing in gamepad mode):
https://www.esoui.com/downloads/info2540-ConsoleFonts.html