I too have an ancient OptiPlex 360 with a 3.33GHz dual processor E8600 CPU that is maxed out at 4GB. It was given to me by a neighbor and had been stripped of the hard drive. I use it only for Node.js development with VSCode but even with minimal use it is struggling against the 4GB limit. I had wondered if 8GB was an option given the chipset and age. I did find an anecdotal report from someone that 8GB was possible if rare and expensive 2x4GB PC2-6400 DDR2-800MHz LOW DENSITY Desktop Memory is used. If I could get the memory for USD$20 I'd give it a shot but the memory I am finding costs more than the machine is worth. In a dozen years the memory will probably be selling for $1 a DIMM but I will have had several newer computers since then.
Top end is
Intel Core 2 Duo E8600 Processor (3.33GHz, 6MB L2 cache, 1333MHz FSB)
Intel Core 2 Duo E8500 Processor (3.16GHz, 6MB L2 cache, 1333MHz FSB)
Intel Core 2 Duo E8400 Processor (3.00GHz, 6MB L2 cache, 1333MHz FSB)
Intel Core 2 Duo E7600 Processor (3.06GHz, 3MB L2 cache, 1066MHz FSB)
Intel Core 2 Duo E7500 Processor (2.93GHz, 3MB L2 cache, 1066MHz FSB)
Intel Core 2 Duo E7400 Processor (2.80GHz, 3MB L2 cache, 1066MHz FSB)
Upgrades are not very expensive.
RAM is a Major Limiting Factor
Listen to these people and DO NOT upgrade anything on a system this old.
The components are expensive, you will not even notice the "upgrade" and you may spend more than it costs for a newer refurb Dell Optiplex. Recently Dell had a 40% off sale where you could get 4th-Gen i5 quads (like a world faster than yours) for less than $150.
Do not sink another penny into your current system, and just use it as-is, while saving every penny for a newer one. Whatever cash you sink into a system this old is 100% wasted - I guarantee it. It's just an illusion that will cost you a lot of wasted money.