I suspect that a popular app is styling highlighted text this way. Do you know it?
I noticed it first in this tweet:
Then I saw it again in this video:
The line style is called round line caps in SVG parlance:
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I don't think it's a trend, just a matter of practicality/convenience.
Firstly, I reckon it's not a vector line with end caps, because the text is quite obviously scanned or photographed, and the highlight has probably been added using a raster image editor like Photoshop or GIMP (or virtually any half decent raster image editor) using a round brush tip. No need to worry about end caps.
You can add a new layer, set the blending mode to multiply, choose a round hard edged brush, and click once for the start of the line, hold down Shift, then click a second point to make a straight line between the two.
So, if I were to hazard a guess at its origin, I'd say it was probably with the advent of image editors like Photoshop, which gained layer functionality back in 1993 (Photoshop 3.0 introduced layers). It makes sense to use a round tipped brush to do this, because a flat edged brush would need to be specifically created/rotated to make sure it's at the correct angle, introducing an unnecessary complication. Obviously a round brush tip is more practical to use to highlight text, especially if it's sloping downwards as in the example.
Photoshop with coloured rounded rectangle overlayed probably. Can be done in just about every photo editing app.
As you can see from the woncky angle it is a picture and not live digital text. Colour overlay is also not perfectly aligned with text angle – which you would expect from an app that highlights the text.