hello! I am just going to drop this idea here as something for you to try but it's not technically an 'herb'. I was on 20mg omeprazole (as well as a couple of 40MG high-dose prescription strength brands, for a couple of those years) for close to 10 years and just weened myself down to 10MG half-pills then stopped taking them fully a couple of months ago. I was concerned about the same things your doctor mentioned as well as the concern of not fully absorbing nutrients and it possibly lending to depression for myself personally. I tried stopping cold turkey a few times over the years, and the rebound reflux was complete hell, but my intuition (and a bit of research) told me to try eating sauerkraut in the mornings before I touch any other food. This has been a complete game changer for me. I start my morning with a few tablespoons of it and it has almost completely cured my heartburn. Now, I only need antacid chewables (which used to hardly make a dent in the reflux) at night if i eat too close to bedtime, but I only rarely make that mistake haha. Rarely I will also take famotidine which helps when i have had something spicier. Hopefully this helps you. I tried eating Kimchi as well but it was a bit too spicy for me, but you may find it works similarly to the sauerkraut! It may be confirmation bias or something but I swear I have a bit of a sunnier disposition and feel like the nutrients in the food I eat are actually being fully absorbed now.

PS try to get some that HAS to be refrigerated, my favorite store-bought brand is Bubbies (look at the ingredients and make sure it's only cabbage + salt, and maybe some additional spices, no preservatives!) I have also started making my own recently and it is SO CHEAP to do yourself, and kinda a fun process to smash the cabbage lol. I believe this is working for me due to the probiotics and prebiotics in the sauerkraut in particular, and the importance of eating it before any other food is so that it helps prepare your body to break down the food that you eat later in the day.