is a 30” trenching bucket too big for a 580c
Loading mulch into trailers, no. Digging trenches in rooty and rocky ground, yes.
No, but it will be challenge to learn it's limitations. Like how much material you can put in it and how far you can extend the hoe without tipping.
I have a 14' hoe on my 931B that is similar and it handles a 30" bucket OK. In hard digging you need to keep it closer to the machine instead of reaching way out. Good teeth make a big difference. Specs list HD trenching bucket up to 36". You should be fine in all but the most extreme digging conditions. https://machine.market/specification-213