When Blender renders an animation into a sequence of images, it saves certain information, including render time, into each image's header. Total Render Time reads that metadata. In a single button click, it checks your render directory, lists all the files inside, adds up the render time across every file, and reports the total.
The add-on works when you render to JPEG, PNG, or OpenEXR, which covers the vast majority of animation renders. It's limited because Blender can't always save render information. For example, it doesn't write render time into TIFF headers. If you use another format that stores render time, which you can confirm by loading an image into the sequencer and checking for information around it, the developer invites requests to add support in a future release.
Built by Moby Motion for Blender 3.3 and released under the GPL license, Total Render Time ships with documentation. It's a Dev Fund contributor entry in the superhive library.