Earlier quoted context omitted.
"All images are deleted after 1 hour" - so they're using a server and it's a valid ask. My question is - why does this require a server? Write it in something that compiles to LLVM / WASM and just make a static page. Infinitely scalable and just pay for the domain (and CDN provider if applicable) both likely nominal cost.
It can pull images from a domain. That would be difficult (since for client-side rendered sites it would require loading the site in a sandboxed environment) or impossible (if the site actively prevents that using CORS or similar, or if it happens to include scripts which expect to be run in a normal environment).
You might still be able to offset a portion of the compute by just figuring out the URLs of the images on the back-end, sending that list to the client, which would then download and do the optimization / resizing.