Simple answer - probably.

The advice is the smallest dose that works. That usually means to suppress any acid reflux symptoms but if you don't feel any the lowest possible dose is probably sufficient.

Anxiety is common amongst those diagnosed with Barrett's. It can also exacerbate acid production.
PPIs like omeprazole have been shown to probably reduce risk of developing cancer - possibly by reducing risk of oesophagitis triggering production of more Barrett's cells which all have a very slight possibility of mutating towards cancer.

More important are the surveillance scopes every few years to confirm the Barrett's cells remain unchanged. And, the longer you've had Barrett's, the lower the risk of it mutating.

Those symptoms could be from reflux but not acid so 10mg omep is probably sufficient.
As to trigger foods, it doesn't sound as if you have any. No need to avoid anything. Because they appear on lists that others find are triggers doesn't mean they're pertinent to you.
This is from a recent discussion paper: "Often there is a lot of counseling about foods to avoid, and really, the evidence is against doing that. If patients identify specific food triggers for their symptoms, then great. Don't eat that stuff. But in terms of making blanket statements about foods that trigger heartburn symptoms, that counseling tends to not be useful."

Yes. 20mg panto = 10 omep. If you're not getting burning (heartburn) pain, it should be sufficient.

You appear to have identified the cough is from reflux and are taking lifestyle measures to reduce that. PPIs like pantoprazole do not stop the reflux, just make it less damaging.

I can sympathise as your condition sounds much as mine was 12 years ago. The cough can certainly be debilitating and is the most common symptom of reflux that has porgressed to breach the upper sphincter and aspirate into the respiratory system.

Like you, I have had my Barrett's a long time (at least 26 years and probably much longer). In my case, the doctors tried to stop my cough by increasing the dose of my omeprazole (to 80mg daily) ineffectively. I would get coughing fits daily lasting 2 hours at a time and ending with me nearly passing out. I would sit up from 2 - 4:00 every morning coughing.

Lifestyle measures were doing nothing for me, the condition was getting worse and I asked for, and eventually received, a fundollication.
All my symptoms of extra-oesophageal reflux vanished overnight.
(You may read my account of that operation
here amongst a number of others.)

Hoping you find treatment that works for you soon.