I am familiar with several commands like
free, etc. However, is there a command to see the peak/burst memory usage of the entire server (not individual processes) over, say, the last 30 days/24 hours/etc.?
You'll need to collect these metrics.
Sysstat may do this assuming you can define a couple crontabs.
We could also mention Netdata: even though that one won't keep histories, it's still pretty helpful graphing instantaneous resources usages.
atop tracks historical metrics and is command line based.
It's packaged in Debian/Ubuntu and Fedora.