If I start a showdown and tap Honey Fruit to gain resources, would that result in my chain ending and result in focus passing to my opponent?

To answer your question, we first need to look at how Honeyfruit functions within a showdown.

According to the card text: "[T] : [Add] [A]. (Abilities that add resources can't be reacted to.)"

The Ruling

No, your chain does not "end" in the way you are describing, and Focus does not pass to your opponent as a result of this specific action.

Here is the breakdown of why:

1. "Add" Abilities skip the Chain/Priority process: Your card note and the core rules specify that abilities that "Add" resources (like Honeyfruit’s ability) resolve immediately upon finalization. They do not enter the chain in a way that allows for reactions or priority passing steps (Rule 337.1.c).
2. Focus/Priority rules: Because "Add" abilities finalize and resolve immediately, they do not create a standard chain that requires players to pass priority or shift Focus. Rule 346.1 confirms this: "Focus will not pass in this way if the chain opened as a result of ... an Add ability being added to the chain."
3. Showdown state: Since you are in a Showdown, your state remains "Open" after the Honeyfruit ability resolves, and you retain Focus. You are free to continue acting or to pass Focus to your opponent afterward.

Summary: Using Honeyfruit in a showdown is a "silent" action. It provides you with the resource immediately, does not open a chain for your opponent to react to, and does not cause you to lose your Focus. You will still have Focus after using it.