When you see this on the explorer, what does it mean?
"This transaction is made through Merkle and is not shared to the public transaction pool"
"is not shared to the public transaction pool" probably means that transaction never broadcasted to any Bitcoin nodes and directly added on a block by certain mining pool. The other part doesn't make sense to me though.
This means the transaction is verified using a Merkle tree structure without broadcasting it to the public blockchain.
Your post doesn't make sense, you don't need Merkle tree structure tree to verify transaction. Although it's worth to mention SPV wallet use Merkle tree structure to verify whether certain transaction actually included in a block.