I appreciate the thoughtfulness. I'm not dead set on self hosting - I figured that the relatively simple functionality might already exist in some tools. The client side of the solution would involve no interaction which is why I considered the self hosting route. If the server goes down, as long is it continues to display the time/date/last know notes/messages without any intervention then it would meet our needs. A dashboard tool that runs some elements independently and queries a server for updates on occasion.
I did find MagicMirror, which looks like it could be set up with an SBC connected to a monitor. I haven't yet had time to dig in to its workings to see if would meet the offline/online requirements.
I also found calendarclock.app which, while not self hosted, is purpose built for this scenario and would allow the recycling of existing hardware.
Similar to atzanteol's reply, I appreciate the thoughtfulness you put in to this. Our use case is luckily not so severe as needing reminders for important tasks (medication, eating, etc)... yet. A dumb clock would almost meet our needs, save for the desire to leave notes about our interactions (remembering when we last talked/saw each other is the major stressor).