What is the specific name for curved arrows in diagrams?

The usual term is arrow or connector in diagramming software, but a curved one has a more specific name: a curved connector (also called a curved arrow or arc arrow). In flowchart and diagram conventions, the curved shape is a Bezier connector, since it is drawn with Bézier curves, which is how tools like draw.io, Visio and Lucidchart define it. In scientific figures, especially chemistry, a curved arrow showing the movement of electron pairs is called a curly arrow (or curved-arrow notation, used in reaction mechanisms).

So the most precise answer depends on the field: curly arrow in chemistry, curved connector or Bézier connector in software diagrams.

Since you asked about these curved lines: they're now built into Drawings. Select a connector (or several at once), open the Route menu and pick ⌒ Curve, and it draws as a Bézier curve that leaves and arrives square to each shape, so busy diagrams don't pile their lines on top of one another.

Also, when Daedalus rebuilds a diagram from a picture (the 📷 in his panel, or Import › picture), three optional boxes appear next to the picture: curved connectors, centered container names, and containers that grow to wrap their items. All are off by default, so a rebuild stays exactly as drawn unless you tick them. Curves also export to draw.io.