Everything described here sounds like your team, your extension, and your software development process are the problem. Demanding >9GB of disk space to build a browser extension is capital F, capital I Fucking Insane. Go yell at the Rust folks about their shitty toolchain and your engineering lead for buying into it instead of blaming people who have enough problems as it is just coming into contact with the quagmire you described.
The 9GB limit was not just the Rust stuff, that was for the entire docker environment with compiler, JRE, node, wasm toolkit, typescript, webpack etc. Yes, we need all of these to make a "true" reproducible build from scratch.
> to build a browser extension
It shares 99% of code with a desktop application; you can compile it to wasm while preserving most features. The extension wraps the wasm.
For reference, when making a single clean build, the `target/` dir reaches 700MB.