cloud_api_client: Implement Wasm support (#61328)

Release Notes:

- N/A or Added/Fixed/Improved ...

---------

Co-authored-by: Gaauwe Rombouts <mail@grombouts.nl>

.github/workflows/run_tests.yml

@@ -660,7 +660,7 @@ jobs:
         R2_SECRET_ACCESS_KEY: ${{ secrets.R2_SECRET_ACCESS_KEY }}
         SCCACHE_BUCKET: sccache-zed
     - name: run_tests::check_wasm::cargo_check_wasm
-      run: cargo -Zbuild-std=std,panic_abort check --target wasm32-unknown-unknown -p gpui_platform
+      run: cargo -Zbuild-std=std,panic_abort check --target wasm32-unknown-unknown -p gpui_platform -p cloud_api_client
       env:
         CARGO_TARGET_WASM32_UNKNOWN_UNKNOWN_RUSTFLAGS: -C target-feature=+atomics,+bulk-memory,+mutable-globals
         RUSTC_BOOTSTRAP: '1'