WetGeek There might be a way to bind a keypress to a command on Solus, but if there is, I haven't found it yet.
Found it! Well, not a general case, but for the hibernate purpose we've been talking about.
In the System Settings, Power Management section, there are some settings like this:
I assigned "hibernate" to both of those settings, and it works great! If I just close the laptop lid, it hibernates, and then restores when I open it the next time. If I don't want to close the lid, I just press the power button, and it likewise hibernates until I push the power button again.
These are from the Plasma system settings, but I'm pretty sure every DE will have similar system settings.