How to system test server and Wasm client in headless browser?

I have a server written with tide, that serves a single page web app implemented in seed as a wasm module. I would like to write system tests by starting the server, starting a headless browser, requesting a Wasm test suite and executing those tests.

I know of wasm-pack, which can be used to execute Wasm tests in a headless browser (wasm-pack test --headless --firefox), but this starts a default server which only serves the Wasm package.

I could write a script starting the server in some testing mode, then starting firefox in headless mode and tell it to request the server testing route, but I would like to use existing software, that might support multiple browsers. Is there something like this?