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.