I can't see if anyone else has mentioned it here, but I have had most success with trying new foods in between meals rather than at mealtimes.
Presenting them with an unfamiliar food when they were hungry massively increased the anxiety around trying them - they wanted something familiar because they were hungry and I had cooked a whole meal and didn't really want to cook something else if they didn't like the new element. So we were all over-invested in the situation and the stakes were too high.
Trying new things outside mealtimes really took the pressure off - we could cook together and not be stressed because I was not trying to get a meal on the table as well. We could take the time to try different versions of the food (e.g wedges in different shapes, cooked for different lengths of time, salted/unsalted, skin on and off, crinkle cut etc) and then it's more of an experiment as in 'how are they different and what has made that difference?' rather than the binary options of liking it or not.
I also had to get over my idea of what a healthy diet involved. My two would always eat something from each food group, so I had to put aside my preference for them having variety in favour of their preference for eating familiar and 'safe' foods. They did get bored of something every so often, which led to a natural desire to try something new, but if they hadn't, they would have been getting everything they needed, it was just a bit boring.
I also encouraged them to prepare their own food as much was possible and age-appropriate. I explained that I didn't mind if they wanted to eat the same things, but that I would appreciate help preparing them so that the burden of accommodating that didn't fall solely on me. They understood and were usually happy to help. On days that they didn't feel like it, it incentivised them to try new things.
Providing scenarios where they genuinely saw the benefit of having a broader diet was definitely more successful than any of the many other angles I tried as well.
We talked about the kind of food that they see on cafe menus etc and they were quite keen to try things that they might be able to eat when out. Likewise, they love a picnic, so are more willing to try things like sausage rolls etc when I explained that I would be more inclined to go on picnics if they liked some foods that were easier to prepare/transport/eat than their current favourites.
I try to be honest with them without manipulating them or making them feel guilty - I want them to have a wider diet, but not at the cost of our relationship, but I do give them some idea of the extra work involved in making them different foods so that they see the wider benefits of being able to eat a broader range i.e that we have more time to do other things and (in non-covid times) that it makes more fun stuff accessible if we can be flexible about food.
They cook for us now - mostly they won't try it, but they love making us dinner and it's a really low-pressure way for them to play with new ingredients, get used to the textures and smells of food with no pressure to eat them or even anticipation that they might! It's definitely made them less wary of some foods that they had some pre-conceptions about so I live in hope that we will one day find a meal that we can all eat together!