What I use to view videos on the SD is VLC (I am using Windows, I haven’t tried other platform distributions)
With VLC you can open a folder and it will load all the videos in the folder and its subfolders into a temporary playlist. When you play, it will automatically advance to the next when the previous is done. But each one minute segment plays separately with its own play bar; it doesn’t create a “virtual single video”, so you can’t “scrub” across individual segments by dragging the cursor (at least that I am aware of).
I haven’t tried yet, but what I would most likely use to “combine” the 1 minute video segments would be ffmpeg (free and open source, multiplatform) https://www.ffmpeg.org/
The downside for a lot of people is that ffmgeg is a CLI (Command Line Interface) utility. For me, that is an advantage, because it makes it much easier to script than a GUI. But for users that have never used a CLI it adds another barrier to entry. ffmpeg also has a steep learning curve, but google will let you find examples.
Here is one good place to look: https://github.com/amiaopensource/ffmprovisr
And there are GUI front ends available that use ffmpeg underneath to do the work. I haven’t used them, but google will find them. If anyone has a recommendation, chime in with a reply.