Selfhosted

Solving it the unix way:

ls -1 | sort -R | sxiv -f -s f -S 5 -

So it's ls -1 to list the content of current directory (presumably where your pictures are), with one file per line, so we can then pipe it to sort, with the -R option to sort randomly, then piping the result to sxiv, a lightweight image viewer available on most distro (I just checked, it's available on Debian). For its options : -f means it's fullscreen, -s f makes it scale to fit the image on screen as well as possible, -S 5 tells it to start in slideshow mode and change picture every 5 seconds, and - is to tell it to take the files list from stdin (thus from the ls and sort commands).

This won't work for videos, though, only pictures.

https://github.com/meichthys/foss_photo_libraries

Probably nobody's first guess, but Plex can do this, no problem. It's quietly robust.

Take a look at Photostructure... I think that will meet your requirements!

you can use qiv , it's in the repos

Photoprism can do random slideshow in the library/browse?order=random endpoint

https://github.com/photoprism/photoprism/commit/47defc861c17ca1348eb0193b9ea84ce2708f228

You didn’t say anything about price, so I’m going to offer Chevereto.

If you want slideshow on android device, there is an app on gstore called photocloud. It can play from shared folder or nextcloud for example. Looks outdated but it has features you want. There is a downside tho

Pricing

Pricing: free version shows a “please purchase” images once a while during the slideshow. There is an in-app payment which removes these images. Another payment unlocks the “Daydream” functionality; this only works on Android 4.2 and higher, don’t purchase if you have Android 4.1 or lower.

Not exactly what you asked but it might be usefull