Sorry I cannot help you too much, but I'll offer what knowledge I have.
I do not own an RG35xx and I've never used Batocera. Checking multiple locations (why is it so hard to find this info?), it seems as though Batocera should have some form of sleep function on 5.30 and later, but I cannot find any mention of this in any change logs (nothing about it in the 5.30 change log) and I looked through a lot!
Garlic OS does have a sleep mode built in to the CFW. I cannot say for sure how effective it is.
Please note that Linux retro handhelds (at least, every one that I've ever owned and every CFW I've ever tried) do not have a true sleep function like Android. Every Linux sleep mode I've tried has been a hack of sorts that is just trying to turn off as many things as possible (screen, sound, wifi, bluetooth, control triggers, etc.) in an effort to try and save as much battery as possible. These "sleep modes" will be instant on and off, because they are never really off. On my Miyoo Mini Plus, I can easily lose massive amounts of battery while in "sleep mode" depending on the game. I believe our batteries are close in size, so you might have the same issue.
If you really, really need an instant on and off and a true sleep mode, you should prioritize Android OS for your handheld. (Don't forget, some Anbernics can dual boot Android and Linux!)