Why would you need Codespaces for that? They released a standalone GitHub app recently just for this purpose. Not sure if it also works with the web version. But Codespaces seems to be the wrong tool for this job.
Their app is still outrageously feature incomplete in some ways. Can't create a branch! Can't edit files! Still better than their mobile site though but I end up opening their site in desktop mode to do any real work on my mobile. Super annoying!