Auto Stop Free is a Blender add-on from Coby Randal Media that places a single checkbox in the 3D Viewport N-Panel. With it enabled, animation playback and recording stop at your scene's last frame instead of looping back to the start.
That stop matters for auto keying work: Blender's default playback looping can overwrite auto keying input, and it can cause rigid body physics simulation caches to be lost. Halting at the final frame keeps both intact so you can focus on your performance.
Legacy support for Blender 2.79 is included, which allows live interactive physics that can be imported into later Blender versions for rendering in Eevee, Cycles and beyond. The add-on covers Blender 2.79 through 5.1, ships under the GPL license, and comes with documentation. It is one part of Coby Randal Media's line of auto keying tools, alongside Countdown Record + Auto Stop and Camera Flow Pro.