Having a similar issue, except using gpucomputationrenderer from 'three/examples/jsm/misc/GPUComputationRenderer.js' and not the drei hook. Disabling StrictMode doesn't seem to fix it in my case. Only the first gpgpu variable texture actually updates and then the compute chain seems to break. It worked perfectly in the three.js version but something breaks in r3f.
Can't seem to find a solution atm. Found this implementation though: https://codesandbox.io/p/sandbox/admiring-christian-nnxq97?file=%2Fsrc%2FuseGPGPU.ts, and I followed it. The structure of implementation in the example works in the sandbox version but not in my app. Maybe this example could help you.