perf(trie): fix allocation hot paths with capacity hints and buffer reuse

- Replace clone() with mem::take pattern in update_account and
  update_account_storage_root to avoid buffer cloning on every account update
- Add capacity hints for child_stack, retained_proofs, and rlp_nodes_bufs
  in ProofCalculator to reduce Vec reallocation overhead

Amp-Thread-ID: https://ampcode.com/threads/T-019bfe25-43f3-75ac-98f7-32bf937b69e1
Co-authored-by: Amp <amp@ampcode.com>

crates/trie/sparse/src/state.rs

@@ -884,9 +884,12 @@ where
 
         trace!(target: "trie::sparse", ?address, "Updating account");
         let nibbles = Nibbles::unpack(address);
-        self.account_rlp_buf.clear();
-        account.into_trie_account(storage_root).encode(&mut self.account_rlp_buf);
-        self.update_account_leaf(nibbles, self.account_rlp_buf.clone(), provider_factory)?;
+        let mut rlp_buf = core::mem::take(&mut self.account_rlp_buf);
+        rlp_buf.clear();
+        account.into_trie_account(storage_root).encode(&mut rlp_buf);
+        let result = self.update_account_leaf(nibbles, rlp_buf, provider_factory);
+        self.account_rlp_buf = Vec::with_capacity(TRIE_ACCOUNT_RLP_MAX_SIZE);
+        result?;
 
         Ok(true)
     }
@@ -937,9 +940,12 @@ where
         // Otherwise, update the account leaf.
         trace!(target: "trie::sparse", ?address, "Updating account with the new storage root");
         let nibbles = Nibbles::unpack(address);
-        self.account_rlp_buf.clear();
-        trie_account.encode(&mut self.account_rlp_buf);
-        self.update_account_leaf(nibbles, self.account_rlp_buf.clone(), provider_factory)?;
+        let mut rlp_buf = core::mem::take(&mut self.account_rlp_buf);
+        rlp_buf.clear();
+        trie_account.encode(&mut rlp_buf);
+        let result = self.update_account_leaf(nibbles, rlp_buf, provider_factory);
+        self.account_rlp_buf = Vec::with_capacity(TRIE_ACCOUNT_RLP_MAX_SIZE);
+        result?;
 
         Ok(true)
     }

crates/trie/trie/src/proof_v2/mod.rs

@@ -105,10 +105,10 @@ impl<TC, HC, VE: LeafValueEncoder> ProofCalculator<TC, HC, VE> {
             hashed_cursor,
             branch_stack: Vec::<_>::with_capacity(64),
             branch_path: Nibbles::new(),
-            child_stack: Vec::<_>::new(),
+            child_stack: Vec::<_>::with_capacity(64),
             cached_branch_stack: Vec::<_>::with_capacity(64),
-            retained_proofs: Vec::<_>::new(),
-            rlp_nodes_bufs: Vec::<_>::new(),
+            retained_proofs: Vec::<_>::with_capacity(64),
+            rlp_nodes_bufs: Vec::<_>::with_capacity(8),
             rlp_encode_buf: Vec::<_>::with_capacity(RLP_ENCODE_BUF_SIZE),
         }
     }