there are a lot of choices in the market, my view is to decide on a particular platform and dive deeper into it, select one that fits your need, and especially as an immediate step that you are interested in, or you have built previously.
I'm going to focus on finding the option that has better viability and might have a better chance to port onto multiple platforms (Web, Mobile, Desktop), and also to integrate with your current website, mobile app, or any backend system.
I'm particular in favour of a client and server model. One may start from the game client development, be it from offline, then integrate with some online tools, database, backend, allow sign-in, high score, leaderboard, then eventually for multiplayer gaming.
to start with the game development, a few Game Clients development choices that I came across would like to highlight are
Game Client Development Reference
a few that intrigues me - Phaser, Unity, and Godot.
has expanded quite aggressively and powered many games nowadays, since I get to know about it nearly a decade ago. I was once a Unity Developer, and it was my primary game editor. Nowadays they offer plenty of learning resources on their site to help people to pick up the tool. Aside from that, is that required to dive really dive into the C#? I think that shouldn't be an obstacle. The programming syntax could be learnt passively. As you have a goal and idea that you want to implement, checking out examples, and reference, you would get it there, and the learning process would have been more fun compared to reading through all the language tutorials.
I recommend it first, because it has a rich ecosystem, and many SDK support for various cloud integration, and client development, for example, integrating with Firebase, AWS, or maybe the Google Play SDK. Another plus point is that Unity seems to be possible to plug into the Flutter app , with this Flutter widget
Godot shines in the open sources space and has a very permissive MIT license. I do have the dilemma of whether to invest time and energy to start with this platform. because of possibly lighter weight, more manageable project files, and the simplicity of the tools. its editor has a more cosy layout, bigger font, and space but is just a little, it's an all-in-one tool, code and design in the same editor. Everything looks simpler, however, I also observe that being in the open-source space also meant that the development pacing can be slower compared to the commercial counterpart.
Backend Game Server
usually, when we're thinking about building a game server backend, there goes the Authoritative Server. PUN/Photon engine has a very good explanation about this
in fact, one could possibly consider Unity + Photon.. just in my case, I have some doubts that I wish to build it along with other NodeJS solutions, and integrate some existing work with it. Hence I found an alternative, which is Colyseus
perhaps that it was built on NodeJS, that is what appears to be interesting, having room for expansion and writing custom codes.