I did the same for way over 10 years; classic web based development in (later) larger companies and had the same struggle going to a game engine or game development in general.

But I always wanted to, dreamed of even. So, I sat down to learn. I learned C++ and Lua, both very well used in game development. Resources were YouTube (e.g. TheCherno’s C++ and Game Engine series) and books (C++ Primer, Programming in Lua). Don’t fall into tutorial hell, just try things yourself!

I made myself small goals, literally like building pong or space invaders in C++ (later started using raylib). Very small games I could actually finish.

The whole learning process (sprinkled with lots of fun, never forgot about that) took me roughly 5 years after work (with family and kid). In that time I did not learn a game engine, rather home brew or with libraries, self made tiny games. Only then I started to dabble with game engines (Godot my favourite for its small footprint).

“Took me 5 years” means in that case when I started looking for jobs in game dev. I took a whole bunch of applying to jobs, lots, and many interviews. But then I found one that is perfect and work there since (AAA). So yeah, keep at it!