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Have you ever heard of dear Imgui?
There's a full example of one way of doing text rendering in this repository: https://github.com/JoeyDeVries/LearnOpenGL under src/7.in_practice/2.text_rendering/
Storing all glyphs in a single texture like you describe is also commonly done. Another piece of code you might want to have a look at is freetype-gl: https://github.com/rougier/freetype-gl.
Take a look here for some guidelines and samples.