chore: update crates.io publish plan and fix dependencies

- Update CRATES_PUBLISH_PLAN.md with Level 0-2 completion status
- Fix binary-merkle-tree and related dependencies
- Add runtime_logger_tests.rs
- Update various Cargo.toml files

bizinikiwi/primitives/runtime/src/proving_trie/base2.rs

@@ -23,7 +23,7 @@
 use super::{ProofToHashes, ProvingTrie, TrieError};
 use crate::{Decode, DispatchError, Encode};
 use alloc::{collections::BTreeMap, vec::Vec};
-use binary_merkle_tree::{merkle_proof, merkle_root, MerkleProof};
+use pez_binary_merkle_tree::{merkle_proof, merkle_root, MerkleProof};
 use codec::MaxEncodedLen;
 
 /// A helper structure for building a basic base-2 merkle trie and creating compact proofs for that
@@ -143,7 +143,7 @@ where
 		return Err(TrieError::ValueMismatch.into());
 	}
 
-	if binary_merkle_tree::verify_proof::<Hashing, _, _>(
+	if pez_binary_merkle_tree::verify_proof::<Hashing, _, _>(
 		&decoded_proof.root,
 		decoded_proof.proof,
 		decoded_proof.number_of_leaves,

bizinikiwi/primitives/runtime/src/runtime_logger.rs

@@ -62,40 +62,3 @@ impl log::Log for RuntimeLogger {
 
 	fn flush(&self) {}
 }
-
-#[cfg(test)]
-mod tests {
-	use bizinikiwi_test_runtime_client::{
-		runtime::TestAPI, DefaultTestClientBuilderExt, TestClientBuilder, TestClientBuilderExt,
-	};
-	use pezsp_api::ProvideRuntimeApi;
-	use std::env;
-
-	#[test]
-	fn ensure_runtime_logger_works() {
-		if env::var("RUN_TEST").is_ok() {
-			pezsp_tracing::try_init_simple();
-
-			let client = TestClientBuilder::new().build();
-			let runtime_api = client.runtime_api();
-			runtime_api
-				.do_trace_log(client.chain_info().genesis_hash)
-				.expect("Logging should not fail");
-		} else {
-			for (level, should_print) in &[("test=trace", true), ("info", false)] {
-				let executable = std::env::current_exe().unwrap();
-				let output = std::process::Command::new(executable)
-					.env("RUN_TEST", "1")
-					.env("RUST_LOG", level)
-					.args(&["--nocapture", "ensure_runtime_logger_works"])
-					.output()
-					.unwrap();
-
-				let output = String::from_utf8(output.stderr).unwrap();
-				assert!(output.contains("Hey I'm runtime") == *should_print);
-				assert!(output.contains("THIS IS TRACING") == *should_print);
-				assert!(output.contains("Hey, I'm tracing") == *should_print);
-			}
-		}
-	}
-}