Spot on with the recovery mode instructions. I've noticed that while the wipe itself is quick, that initial splash screen on reboot is where people usually panic because it hangs there for a while. It's totally normal though, basically just the OS setting itself back up from scratch. From a technical standpoint, the S10 uses UFS storage so it's usually pretty efficient, but if your storage was nearly 100 percent full, the file system might take an extra minute to sort itself out during the wipe phase. Quick question tho, are you doing this to solve a specific performance issue or are you getting ready to pass the phone on to someone else? Also, did you already make sure to remove your Google account in settings first? If you dont, you might trigger the Factory Reset Protection lock which is a whole other headache.

A factory reset on an S10 usually takes a few minutes, but larger data amounts can increase this. If it takes excessively long, force restart your phone. Yes, holding power and volume up simultaneously enters recovery, where you can select "Wipe data/factory reset". Remember this erases everything! If the boot loop persists after the reset, check recent forum discussions as Odin may not be a solution.