This may be a silly question, but I was wondering today… if I have a working installation with some packages installed already on my Raspi 3 and I decided to insert that same SD card into a Raspi 4. Would it boot up and work without issue? or are there some hardware-specific packages that would break the install from working properly?
It depends, I would say.
It can work like here: https://www.reddit.com/r/dietpi/comments/tadys7/pi3b_pi4_upgrade/
This thread mentioned it is not possible, but this post is somewhat old.
Make a backup and just try it 
Don’t trust external source 
Yes it is working, usually. It depends of your image is an older one. But normally it’s working ootb without any additional steps needed. You can simply move the SD card and give it a try. The only thing needed, would be to install RPi4 EEPROM firmware once system is online on the Rpi4. This can be simply done using dietpi-config
Fantastic, I’ll give it a shot.
BTW, I’m familiar with dietpi-config, but I haven’t noticed the RPi4 EEPROM option - is this only there when using a Rpi 4? 
yep should be available on the RPi4 once online.