These methods involve using hardware wallets, QR codes, or mesh networks to facilitate transactions offline, but they still require an internet connection at some point to broadcast the transaction to the Bitcoin network for verification and confirmation. Or what's your take on this.?
You are right. At some point, we do require an internet connection to broadcast the transaction over the internet.
I have even read about sending bitcoins through SMS which is then used by some resource to make the transaction.
So there are methods which indirectly broadcasts the transaction to bitcoin blockchain but internet is still required at some point.
There is no way we can create a transaction on bitcoin blockchain without the use of internet.