Someone can correct me if I am wrong, but I think that the current traditional way of addressing a hiatal hernia is surgery. If that is the case your doctor may not think the hernia bad enough for that step.

The NIH had a paper on doing the bridge exercise to address GERD: https://pubmed.ncbi.nlm.nih.gov/36311470/. There is also an approved device in Europe used to strengthen muscles and keep GERD at bay. It's called Iqoro. It's not FDA approved and not available in the US. I bought a mouthguard with a strap as a cheap way to see if the Iqoro claim of neuromuscular training would work. Since it can take up to six months to work, according to the manufacturer, and I just started using my knockoff, I can't say whether it's an answer. The mouthguard cost me about 12 bucks if you want to try it. The Iqoro web site gives instructions on how to do the exercise.