Downsite Hibernate usually does not work for me (PC does turn on, but is unresponsive, but this is something that is unrelated (I think)). Interestingly, Hibernate is greyed out for me.
I asked because I've never used Suspend, so I might not be a good source of help for you. At my location, I have 3 computers and 5 virtual machines that are all capable of hibernating, and I normally use that instead of shutting them off when I'm done with them.
Hibernating copies the current session to swap, then turns the computer off completely. On a restart, it fetches the saved copy of RAM from swap. The result is very useful, because your session appears just as if you had never left it. That's why I use it for my VMs, and saving electricity is why I use it on my hardware.
But there must be sufficient swap space for the entire contents of RAM to be saved there. With 32 GB of RAM and a 20 GB swap, that might be why the Hibernate option is grayed-out when you see the above dialog. I use Solus Plasma, and it simply warns me that it can't hibernate in that case. Perhaps this is Budgie's way of telling you that. Maybe too much of your RAM is in use to allow you to hibernate, or perhaps Budgie simply decides whether it can hibernate differently than Plasma does. Perhaps it just compares RAM size with swap size.
The image above is from my Budgie VM, which has 4 GB of RAM and a 6 GB swap partition, so it has no problem hibernating. I love being able to start it up and continue where I left off during the last session. Sadly, though, I have no experience with Suspend. Although I know what it does, there's little chance of my helping you with this problem, because I don't know what could cause it not to work right. Hopefully someone else here will be able to help you with that.