There are tons of possible symptoms because systemic inflammation including from dietary causes basically damages the entire body. But here's a list of some common symptoms from one source:

persistent pain, chronic fatigue or insomnia, joint stiffness, skin problems, elevated blood markers (such as C-reactive protein), gastrointestinal issues (constipation, diarrhoea, acid reflux), depression, anxiety and mood disorders, unintended weight gain or loss, frequent colds or flu.

https://stories.uq.edu.au/research/2023/9-signs-you-have-inf...

For myself, when I eat processed food I mostly feel fatigue and low energy and gastrointestinal pain. But it's been extremely rare for me to eat these things in the last 10 years.

Most of the US population are systemically inflamed including from diet basically all the time, and most of the US population are suffering from several of the above symptoms chronically. (Not to claim that it's definitely or only because of food, but I'd bet it's a big part of it.)

I notice that my allergies get worse, and a theory is that systemic low-grade inflammation and histamine response may be due to diet. I don't have a lot of other conditions, but people with autoimmune conditions (e.g. rheumatoid arthritis) might see it get better/worse with dietary changes.

When I'm eating beans+rice and a bit of protein that I cook myself, my allergies are a lot lower.

When I cheat and eat "crap" I tend to start sneezing and rubbing my eyes.

There are a lot of variables, though, and cheat foods tend to be highly processed, high in gluten, with a lot of additives and made with seed oils, and hidden sugars, and are much higher glycemic index with higher glycemic loading, amongst other things. Plus seasonal allergies are just variable day-to-day which is another confounding factor. So I don't really know what the X factor is. I get similar effects on an atkins-style high fat beef, butter and cheese kind of diet, because it also cuts out most of those things.