I expect eBay require the code so the buyer can't open an item not received dispute

Can you not mark it as 'posted' ?

Though you still have no way to prove it was collected if they open a dispute

All your items show postage as well, did you buyer select the pick up option, or did they choose the item to be posted and then change their mind?

Is that why they didn't (or say they didn't) get a QR code? 

Just mark as ‘sent’

If I buyer wishes to pick up an item, they need to go through eBay’s checkout and select pick up option.  They can either pay then through checkout, or pay cash on pick up. As long as the buyer uses checkout they will receive an email with a QR code or number code.  When they arrive to pick up, the seller needs to use the eBay app in order to scan the QR code or enter the number code.  It won’t work if you use a browser and the eBay website. It has to be done through the app

Anecdotally it’s directly related to paying by one of the payment methods provided in eBay checkout.

❝In addition to paying via eBay checkout, you can sometimes pay for local pickup items by internet banking, cheque or money order – either beforehand or when you pick up your item. Sellers may also accept cash for local pickup purchases.

After you've completed your purchase, we'll send you an email with a local pickup code (a QR code and a 6-digit code).❞

The code is necessary where a seller would be vulnerable to a claim under the MBG. Where that’s not an issue, the seller doesn’t need the code. 

It seems to be the case that unless a buyer goes through eBay checkout to pay via one of the following payment methods, there is no pickup code generated:

• Credit card or debit card
• PayPal
• Apple Pay or Google Pay
• Afterpay
• Zip
• eBay gift card or eBay voucher