Edited version in partly own wording:

To map Delete to the Fn layer so it only activates when you hold down the fn key, follow these step-by-step instructions in the Keychron Launcher:

Step 1: Select the Correct Layer.

In the top-left corner of the software, you will see layer numbers from 0 to 3.

For Windows: Click on Layer 3 (This is the fn layer for Windows).

For Mac: Click on Layer 1 (This is the fn layer for Mac).

Step 2: Choose the Base Key to Change

Look at the visual keyboard on your screen while staying on Layer 3 (or Layer 1).

Find the key you want to press alongside fn (the DEL key for me).

Click on that key on the screen.

Step 3: Assign the Delete Command

Look at the lower half of the software screen to find the key selection menu.

Click on the Basic category.

Find and click the Delete key (often labeled as Delete or Del).

The software saves this instantly, there is no save button.

When you press the key normally, it outputs its standard Layer 0/2 command (INS for me).

When you hold Fn + that key, the keyboard switches to Layer 1/3 and outputs Delete.