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.
To the posters commenting on how amazing it is Americans are wowed by the obvious: there’s an entire electric train network called BART throughout the land surrounding this small peninsula run of Caltrain. And it’s been running since the 60s so it’s not really new to us. It’s also noisy as shit because the wheels are dumb. But it’s still fast.