Not sure if this is acceptable to you, but Uber has a web app at <https://m.uber.com>. I seem to recall that you have to "request" access in order to use it, but it was an automated rubber-stamp thing. The only downside (besides what you'd expect for a web app vs a native app) is that you can't do fancy things like multiple destinations in one trip, or changing your destination on the fly.
Because of this I'd love to see GrapheneOS' sandboxed Google Play Services shims I'd love to see integrated into LineageOS.