The language is irrelevant for as long as it isn't something exotic and runs moderate fast on any architecture. You can make your own engine if you know that you need a special requirement and/or for performance reasons but taking a look at the Pokemon TCG Online or Magic the Gathering Arena for example, both are made with Unity. Also the mobile App from Mansions of Madness was made in Unity (or at least it lokked like it was). Valve's Artifact is made on Source Engine 2

Unity has the benefits of being a good cross-platform Game Engine related to mobile development and you can rapid prototype within it. Godot is quite popular at the moment but as I saw the source code and don't know how well it performs on mobile devices, I would suggest against using Godot and instead go for Unity (which I don't suggest very often except for cases when mobile platforms are involved ?).

I havent used much specialized Game Engines made for board/card games so my knowledge is limited