Not sure what you refer to as Primary & Secondary. In the Networkupstools (NUT) environment they refer to Primary as a system that should be shutdown after a Secondary one, (as described in the upsmon.conf
file).
IDW how you setup the NUT server/client system, but if I understood correctly you did all of this within an LXC on a Proxmox Host Node without changing anything within the Host Node. (You probably achieved this with USB passthrough to the LXC, or possibly you have a Network-connected UPS). If this is indeed the case, then AFAIK you would simply enter the desired shutdown (SSH) command within the /nut/upsmon.conf
file in the LXC, so that in fact the server will shutdown when it receives this command.
You need to test your UPS capabilities, (sending the command manually?) if in fact it is capable of this.
When you enter this command (manually) in the LXC, does it shutdown your Host server?
I must be honest - most of your queries/questions here are not Proxmox-centric, and would therefore be better addressed in NUT/UPS forum etc.
In my setup - I don't really use all the bells & whistles of the Networkupstools - But I simply setup a NUT server on the Host itself (the only inevitable big change I made within the Host), & I have a client within a VM (Home Assistant) that monitors the NUT server & reports/takes actions (shutdown etc.). I find I have absolute granular (programmable) control this way. (OL/OB/LB etc.).
Anyway, I wish you much luck, I'm pretty sure you'll find the right way to proceed.