In Arena battles, you can directly see the effect of berserker on the opposing pet, as their Strength increases exponentially with each triggering of the gene. However, you cannot see this effect on your own pet, leading me to wonder: is Berserker even working at all, or does it simply not display?

I think its working for me. I sometimes get the message "your opponent goes berserk" and a large chunk of my pet's health disappeares.

Yes, I know it shows up in the log. What I mean is that if you hover over the opposing pet, you can see their stats, and you can watch their Strength skyrocket after multiple berserks. I once saw it go above 2000 due to all the cumulative berserks. But if you hover over your own pet, you never see that happen, making it hard to tell whether your berserks are having an impact or not. 

Berserker ability works on your pets too. When your pet goes berserk, you see a message in the log: "You go berserk!" You can also see how the damage increases.

Okay, but I'm wondering why you can't see your pet's Strength increase when it goes berserk? And because the amount of damage the pet does normally seems to vary a lot, it's hard to tell whether it's actually being impacted by Berserker or not. Sometimes the pet even does less damage on the round after going berserk, because of the variation. 

It actually shouldn't be displayed for your opponent either, this info is static. There's some kind of view issue with the opponent's popup, and it shows really weird numbers for berserked pets. It's definitely not +75% that are calculated on the backend. We'll investigate why it behaves this way. Sorry for confusion and thank you for reporting.