We've set up local pick up, local delivery and a shipping option. The option to pick up shows as a tab for the customer to choose. I'll set aside my inventory issues for another post.
A customer has raised with us that he could only see one payment option, the shipping one. Not the local pick up or delivery. He was using GPay. When we test it, everything looks to be working and all options are available.
Note: I had originally set up the shipping zone option named as "collection from market" as a work around while I got the inventory sorted for local pick up.