Metal fences are tricky for groundhogs. my parents have one that is welded wire (comes in a roll) and its not sturdy enough for a fat groundhog to climb all the way up and get over, they aren't the most athletic. once they shored up some holes along bottoms of the fence the groundhog wasn't getting inside anymore.
I have the similar plastic-coated hex but ran a cable across the top because I was thinking about deer. Never knew those porky groundhogs could climb so well. I buried a few inches and that’s enough to keep them from digging it seems.
Run a wire around the perimeter near the top with a fence charger attached and you'll solve that one quickly.
I was thinking barb wire, too. I need to do something because I bought a lot of my fruit trees fall of 2019 and so they should be producing next year and they’re pruned low, not to mention I upped my berry game this year.
Not barbed wire: high voltage electric fence wire. Run a single strand near the top with a charger (you can get solar powered ones if there's no AC nearby) and that will stop them in their tracks.