Hi Ethan,
I went through both the regular User Manual as well as the Hardware Maintenance Manual and could find no indication from HP that there's a CMOS battery inside your computer. At this point the only thing I can suggest is to open it up and physically examine the motherboard looking for a coin cell battery mounted on or near it.
[link|http://h10032.www1.hp.com/ctg/Manual/c04580734.pdf|HP Pavilion x360 Convertible PC Maintenance and Service Guide|new_window=true]
I have noted a trend in a couple of laptops where they've opted not to use a CMOS battery and instead rely exclusively on the main battery to maintain the BIOS and RTC settings. Of course, that means if you remove or unplug the battery for any reason, you have to redo your date & time and any BIOS settings you change.