impl: enable log and mw_log

- Add more logs from the implementation.
- Fix tests.
- Fix building from Cargo and Bazel.
- Disable `score-log` feature in CI check.

Author: arkjedrz

.github/workflows/check.yml

@@ -39,7 +39,7 @@ jobs:
 
       - name: Cargo Clippy
         run: |
-          cargo clippy --all-targets --all-features
+          cargo clippy --all-targets --features logging -- -D warnings
 
       - name: Cargo Fmt
         run: |