1) Can your Hexblade patron be your pact weapon even though it’s sentient?

I’m asking RAW, not "talk with your DM." Thank you for your help beforehand.

Pact of the Blade says "You can’t affect an artifact or sentient weapon in this way" in regards to making a magic weapon your pact weapon.

A Hexblade is a sentient magic weapon, as read in XGtE, "a force that manifests in sentient magic weapons…"

It sounds to me like you cannot turn your patron into your pact weapon, which would be very self defeating because you’re effectively making a contract with a living weapon to be able to better wield other weapons.

Am I interpreting this correctly or overthinking it?