Fuzzy text on external display

System Settings > Displays. Are you using the display at its native resolution? You’ll need to run it as an extended desktop or in clamshell mode (lid closed, external keyboard/mouse and AC power) to do that. If you’re mirroring, it will have to scale the resolution and that can lead to the fuzzy appearance.

In that case, it is the monitor itself. Larger displays with relatively low resolutions are going to look fuzzy. There’s a reason Apple markets their laptop displays as “retina“, which is because the size of the pixels on the display is smaller than the differences your eye can resolve. That’s not the case with the pixels on your external display, so it looks fuzzy, especially in comparison to the Mac’s crisp internal display.

A 13" M3 MacBook Air has a 13.6", 2560x1664 screen that has 224 pixels per inch. Your HP monitor has a 23.5", 1920x1080 screen that has roughly 94 pixels per inch.

I'm guessing that, on your MacBook Air, the default Display Setting corresponds to Retina "looks like 1280x832" mode where text and objects will be sized "as if" the screen had 112 PPI, but will be drawn at 224 PPI detail. Text would be a bit smaller than on the HP monitor, but with the Mac drawing each letter using 4x as many pixels, text would better approximate its font's true shape, and would be sharper and clearer.

The higher PPI density would also make photos look sharper. A modern digital camera might have a sensor with a resolution of 24 megapixels or more. Even a phone camera might take pictures with a resolution of 12 megapixels. Your HP monitor has a resolution of about 2.1 megapixels, but your MacBook Air has one of almost 4.3 megapixels. When a photo application downscaled photos to get them onto your screen, it wouldn't need to reduce resolution as much to get them onto the built-in one.

If that was a cheaper HP display, it may have a larger pixel dot pitch than more expensive display choices and that will impair text clarity. Also, use a microfiber cloth to remove dust from your HP display and ensure that no bright light source is shining on that display. Next, visit System Settings > Displays and experiment with the different display size settings: