How to turn off link preview under cursor?

In the Apple Mail app, there is no way to turn it off unfortunately, it's also compounded because you seem to have the font size increased, which in turn means the already super long link becomes even larger.

The view is there for security to make sure the links go to the places they are supposed to be going to and not scam websites or harmful locations.

You can of course offer Apple Feedback at their Feedback website and if enough people do, they may offer a way to turn it off or control it.

click here ➜ Feedback - Mail - Apple

On Websites the underlying text is usually controlled by the website code. If the item has a title, hovering over it will show the text sent for it. If the game maker is adding super long urls or text it will show up when hovering over the item. Again, this is compounded by the enlarged font size, as they are usually fairly small.

In Safari, links are only previewed if you press and hold on them.

They are not previewed if you are just hovering over them or leave the mouse pointer over them.

So, the way to stop a link from previewing is to not press and hold on it.

If you are referring to something else, then please explain what that is.

The hover tool tips you see on images are because the web developer has used a title attribute within the <img> tag in their HTML. There is no end-user means to suppress these when remotely linked to an email as Apple Mail cannot use specific CSS tricks such as:

img, a.no-tooltip { pointer-events: none; } /* Stops the hover state from triggering the tooltip */

that one can use with browsers that accept external CSS file rules such as Safari.