Solved textures not loading correctly without having to let the button load
them itself. It's quite stupid of me, to be honest. The Button needs a
REFERENCE TO THE TEXTURE, not a reference to a reference to a texture -_-.
sf::Sprite::setTexture(sf::Texture&) just saves a reference to the given sf::Texture& at m_texture.
If I get a sf::Texture instance converted from a reference at the constructor of Button(), and I pass that to setTexture, the reference to that instance is different from the reference it was created from!

This marks the Menu system "working", so we can start converting the menus from MenuManager into states with a Menu like MainMenu, and the LevelEditor should be able to work using this too.