How can I customize icons in the Dock on MacBook running macOS Sonoma?

I used to be able to do this with secondary click on the trackpad to highlight the icon and then move with finger pointer.

Secondary Click has never been required to move icons in the Dock.

Just click and drag. If you wait too long to start moving, you cannot drag. If you have the Force Click gesture enabled (default) you will not be able to drag if you press too hard.

This article from Apple >> Use the Dock on Mac

User wrote " Sonoma 14.3. "

Current version is now 14.5 Sonoma >> Keep your Mac up to date

About the security content of macOS Sonoma 14.5

Always make a Time Machine Backup  before doing any upDates

Specifically

Add, remove, or rearrange Dock items

On your Mac, do any of the following:

• Add an item to the Dock: Drag apps to the left side of (or above) the line that separates the recently used apps. Drag files and folders to the right side of (or below) the other line that separates recently used apps. An alias for the item is placed in the Dock.
• 
• When you drag a folder to the Dock, you can view it as a stack. By default, the Dock comes with a Downloads folder. See Use folders in the Dock.
• Remove an item from the Dock: Drag the item out of the Dock until Remove is shown. Only the alias is removed; the actual item remains on your Mac.
• If you accidentally remove an app icon from the Dock, it’s easy to put it back (the app is still on your Mac). Open the app to make its icon appear again in the Dock. Control-click the app’s icon, then choose Options > Keep in Dock.
• Rearrange items in the Dock: Drag an item to a new location.

Tip: If you use Handoff, the Handoff icon of the app you’re using on your iPhone, iPad, iPod touch, or Apple Watch appears near the right end of the Dock.

What I said earlier is hocus-pocus, at least I think so now.

What seems to be the solution for me is to click and move the icon quickly. Slow, nothing happens. Quick, the icon moves. I don't know what option, if any, distinguishes between quick and slow. Just be quick!

I configure the dock vertically on the left side of my screen. If I click inside the dock app icon moving it fails. If I click to the left of the dock icon (on the app open indicator dot) I can move it. VERY FRUSTRATING to figure out. I'm running Sonoma 14.5, this has been a pain in my keister for quit awhile, probable predating Sonoma.

RB Connecticut wrote:

I configure the dock vertically on the left side of my screen. If I click inside the dock app icon moving it fails. If I click to the left of the dock icon (on the app open indicator dot) I can move it. VERY FRUSTRATING to figure out. I'm running Sonoma 14.5, this has been a pain in my keister for quit awhile, probable predating Sonoma.

Running 1 M1, 1 M2 and 1 M3 all with Sonoma 14.5.

Not issues rearranging the order of Application in the Dock. whether it be along the Botton of screen or in the Vertical position.

You may try the terminal command below

 killall Dock

It does no damage.

It only resets the Dock