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Safari's Favorite's bar only shows the name of the website. Icons may appear in the dropdowns for folders or the main dropdown list on the far right of the Favorites bar.

You can offer Apple feedback at : Feedback - Safari - Apple

If enough people do, they may choose to add the option.

Was the shelf inside the Safari window? Or just on the desktop on the Mac outside of the Mac?

If inside Safari, that is probably just the shortcuts or favorites bar.

You can open the View Menu in Safari, and then click on "Show Favorites Bar".

If it was something else, you will need to clearly explain what it is you saw, and where exactly it was located.

Not in Safari. In Safari, only the Favorites Bar is available.

Are you sure it was Safari? Might you have been using a different browser or app? Firefox? Chrome? Something else?

Are you sure it wasn't the Dock? Normally sits at the bottom, with icons for Apps, but it can be placed on the side of the screen going up and down.

Was it maybe you just had multiple tabs opened in Safari? Tabs will show the website icon. You can click on the + icon at the top left corner of Safari to add a new tab and open a new website in it, which will have an icon placed on the left side of the tab for it.