Depends for which platforms you want to create game for. If it's for web games, you should stick to JS game engines, such as babylonjs Engines like Unity produces binaries that are too big to be competitive for that market.

As a web dev I made two browser games with no framework (for one I used the Matter.js physics engine) and it was a good experience. The browser has great built in apis like the Canvas element so it isn't completely "from scratch", but you'll still get a great sense for the basics of making a game loop etc from the ground up and you can use your previous experience.

I've also played around with Unity a bit but haven't released anything or finished any project. If I wanted to transition to full time game dev I would probably start learning Unreal or Godot as an engine for major projects... or focus on making browser games, maybe with a JS game engine like Melon or Phaser, or continue to roll my own JS games. The big engines like Unity can compile to web but it's a subpar experience and I wouldn't use it if my main target was in browser.

Web devs like us will have some advantages in already being exposed to some of the networking and stuff related to multiplayer, auth, leaderboards, etc.

If you're seriously making that transition, then you should learn one of the two dominant general gaming engines - Unity or Unreal. Both of them have exceptional documentation and can be deployed in a wide variety of platforms.

If you're going from web dev to game devs as a hobby or just fun side thing, then a JS engine like Melon is a good way to dive in and start creating something people can enjoy without serious investment.

If you're just getting started, I'd recommend trying out a few engines to see what clicks (I find it usually takes at least an afternoon to get a feel for an engine). JS engines tend to be easier to get started with as a web developer, but you'll often run into limitations when you start building more complex games.

Depends on where you want to deploy ultimately.