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I occasionally have a word in a headline that is so long, it won't wrap on a phone unless I insert the HTML entity "­" at a location that will enable hyphenation. But I wonder if this "hidden" character interferes with Google's ability to read the text in the headline?
Sounds like a poor theme, you can add CSS for those so they word-break or overflow-wrap and can automatically hyphenate as well. No need to put anything in the titles yourself when browsers are more than capable of handling that problem (non-garbo themes should already have this built in).
You should really make sure your site is responsive and can adapt to different devices and screens not just your particular phone. Just getting a title to wrap on your phone’s screen doesn’t mean it will do the same on the dozen or so other types of devices. If you go into Lighthouse, you can see how your site looks on every type of device. If your site is responsive, the headline will naturally adapt to whatever screen it appears on
Check "view source" in your browser. If you can see that code in your header tags, then Google sees it as well. As others have mentioned, you can achieve this with CSS which won't affect your text in any way for Google.
Turn on word wrap in CSS and problem solved. Your dev will know exactly how to do this. It’s a simple 1-line adjustment to any CSS class.