Your screenshots indicate your S6 Edge is booting up into its Download mode. When it does this on its own that's often an indicator the installed operating system has become corrupted somehow, so the phone simply cannot boot up normally. And just so you're aware, you can manually boot up into Download mode by simultaneously holding down the Volume Down, the Home, and the Power buttons. But it's typically only required when you're trying to flash a different ROM. There's also Recovery mode (from a cold start simultaneously hold down the Volume Up, the Home, and Power buttons). Recovery is used to do fundamental maintenance tasks. See this site for more details on things like Recovery mode, Download mode, etc.:
https://www.hardreset.info/devices/samsung/samsung-g925i-galaxy-s6-edge/download-mode/
Do you keep your phone in a case? If so, take your phone out and see if it will restart normally. Just to eliminate the remote possibility your phone shifted around inside the case, causing those Download mode buttons to be pushed down.
Otherwise, you might want to try flashing your phone with its stock ROM. And for some background so you know what's going on, your phone's internal storage is divided up into several partitions. Most of them are dedicated to the operating system and are restricted access, with one partition set aside as the user's data partition (which is where all your data, like your photos, are stored). When you flash a ROM (with Samsung devices), this only pertains to those system partitions, that user data partition is left as is. So flashing a stock Samsung ROM should leave your photos, but do keep in mind flashing is not a trivial process. If anything goes wrong there's no guarantee your data won't be affected. It's always best to do a full backup before flashing you phone but in this instance your options don't allow for that.
-- One thing you might want to try first is using Samsung's Smart Switch utility to restore your phone:
https://www.samsung.com/us/smart-switch/
If it does work than you're all set. I wouldn't get your hopes up too much but it's worth trying. And when installing Smart Switch to a PC it'll also automatically be installing the latest Samsung driver (which you'll need to do the following).
-- The next thing to try is flashing the ROM. A good source for verified, stock, Samsung ROMs is Updato. I prefer it to sammobile as sammobile intentionally restricts the bandwidth of its upload servers to non-members. Anyway, go here, select the appropriate ROM that corresponds with your particular carrier:
https://updato.com/firmware-archive-select-model?q=SM-G925I&exact=1&r=&v=&rpp=100
It's very important to choose the proper one, ROMs are
not interchangeable with each other. Different carriers rely on different types of cellular networks and the cellular radio chip inside each phone model has to be fully compatible with that cellular network. Each ROM has the drivers, firmware, and apps that matches up accordingly only with its matching phone model.
For a step-by-step guide on how to do the flashing process, see here:
https://updato.com/how-to/how-to-install-an-official-samsung-stock-firmware-using-odin
If you follow the directions properly there's a good chance your photos will still be there, so don't experiment by playing around with various options in the Odin utility.
And just in case, you might want to just use an older version of Odin. That guide article refers to using the latest version of Odin (currently 3.13.1) and it may work out fine for you but previous versions were typically weak as far as backwards-compatibility. Sometimes it's better to use an older version of Odin that corresponds with older hardware. So if needed, you can pick the version you need from here (scroll down to find what matches your situation):
https://www.droidviews.com/download-odin-tool-for-samsung-galaxy-devices-all-versions/
Lastly, if you don't have access to a Windows PC (Odin is a Windows utility) there's an Open Source alternative, Heimdall
https://glassechidna.com.au/heimdall/
Functionally it's the same as Odin, just note that the user interface is altered.