Special relativity definitely overlaps with quantum mechanics and that overlap forms the basis of the math used at collider experiments like those at the LHC. Special relativity is simple with 2 rules that let you derive all the equations: 1) no universal reference frames 2) speed of light is constant.
You’re probably thinking about general relativity which defines gravity through the curvature of space time.
If you think about quantum mechanics existing on some “canvas”, that might look like an interlocking mesh of springs (like something under a bed or cot). You could take your hand and bounces it up and down on this mesh, adding oscillations and creating standing waves in the grid. These oscillations would be different particles (electrons, protons) each with their own characteristic frequency of oscillations. If you add energy to the bed of springs, you can “pop” particles into existence. All these particles actually are are just excitations of the mesh/canvas. As of yet, there’s been no way to define or find the gravity particle on this canvas, so right now the canvas of space time and the canvas of quantum mechanics are two distinct “things”.
No, the analogy is more that the oscillations are themselves the particles.
The addition of energy into a system would be this hand push. The fact that the particles themselves exist means that they are oscillations in this mesh (with some energy/frequency). Interactions with other particles can add or remove energy.
Definitely these canvas metaphor are just conveniences. Also, I got it from Zee’s “Quantum Field Theory in a Nutshell” which is a standard graduate or advanced undergrad level book on QFT.