KDE Plasma: Spectacle
Spectacle is the screenshot app on KDE Plasma, and recent versions can record the screen as well. Open it from the app launcher, pick a recording mode for the area you want, and start recording from there.
OBS Studio
OBS Studio is a free, open-source app for recording and live streaming. It’s available as a Flatpak from Flathub and in many distributions’ repositories. You build a scene from sources, such as a screen capture, a webcam and audio inputs, and OBS records the result to a file. It can capture desktop audio and your microphone, and setting it up takes longer than the other options here.
On Wayland, add a Screen Capture (PipeWire) source. Your desktop then asks which screen or window OBS may use.
SimpleScreenRecorder
SimpleScreenRecorder is a lightweight recorder that walks you through a few pages of settings: the area to capture, the audio input and the output file, then a record button. It was written for X11, so it can’t capture a Wayland desktop properly. On an X11 session it’s quick and light on resources.