From speaking to women of my mum's generation, mixed feeding used to be a lot more common. Certainly both DH and I were mix fed. Perhaps there was less pressure on women in the 70s/80s and breastfeeding wasn't seen as "all or nothing"? I don't know.
But OP - yes, pumping is the way to increase your supply. I did it by hiring a hospital grade double pump and pumping every 3 hours, including through the night. So I'd bf first, too up with formula/ebf if I had it, then express, then wash/sterilise, then almost 3 hours would be up and the process would start again. It was bloody exhausting. Hence why I only managed it with DC1, I think.
When DC2 had the same feeding issues, I tried my best to express as I had with her big brother, but it didn't work. I wonder if it's because I was simply too exhausted with such a ridiculously tough feeding regime, a newborn and a toddler. Hence why DD is now ff.
Do cut yourself some slack, OP. Ultimately, the most important thing is that your baby is fed, and you're healthy and sane. Breastmilk, formula, a bit of both - all are good, nutritious ways to feed babies.