Once I create a segwit transaction v0 (P2WPKH) or v1 (P2TR key-path spend) I do like that (let’s spend a P2TR output):

• Locking Script (of the P2TR output I am spending): OP_1 PK_size PK
• Witness: 1 (witness_count) SIG_size SIG

So I am questioning, the op code CHECKSIG is routinely added when nodes confirm this transaction?

As a result of with legacy P2PKH transaction you’ve got:

• Locking Script (of the P2PKH output I am spending): dup + hash_160 + pk_hash_size + pk_hash + equalverify + checksig
• Unlocking Script: SIG_size SIG PK_size PK

So on this case (P2PKH) there explicitly is the OP_CHECKSIG within the locking script.

Thanks upfront!