Pretty much any time you plug in an HDMI cable it’s possible to damage the port. If you plug and unplug it a lot then there’s more of a chance that something could happen. That being said if you’re being careful then it’s very, very unlikely that it will cause any problems.
That all being said if it’s a first gen PS4 (1000 or 1100 models) those PS4’s have really bad HDMI ports that are much more likely to break than the later models.
Hope that helps!
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