Most image work does not actually need a server. Canvas and WebCodecs decode and re-encode the common formats, WebAssembly runs the compression algorithms, and WASM or WebGPU can run the models behind background removal, watermark removal, upscaling and OCR. That premise is what this whole category is built on.
So the photos, ID scans and screenshots you open never leave your device. Background and watermark removal do download open-source model files into the browser first; the model comes from the network, the image you picked does not.