I think the disconnect here is that people don't consider that almost any action (process) applied to food post-harvest is 'processing' and it is difficult to draw meaningful distinctions between healthy and unhealthy foods based on the 'processed' description.
If you buy pre-cooked chicken breast, for instance, that's 'processed' in at least three ways: it was cut up, it was seasoned (including with salt, which is a preservative,) and it was cooked. Is that bad for you? Maybe, if they add too much salt. Otherwise, it is probably indistinguishable from the chicken breast you might cook at home.
Pasteurization reduces food waste, but it also improves food safety. Are you better off without 'processed' (i.e., pasteurized) eggs if you're making something like Caesar dressing? I'd rather have the 'processed' eggs.
I try not to eat Twinkies, not because they are 'processed' (home-made, scratch-made cake is also 'processed',) but because they contain a lot of sugar and high level of saturated fat. Personally, I try to avoid sugar as much as possible, and if I'm consuming something with saturated fat, like beef, I want to have a meaningful amount of protein.
*Edit*
Before anybody WELL, ACKSHUALLYS my definition of processed here, please refer to page 5 of this[0] document from the US Federal Government which includes the USDA definition of processed food:
A processed food is “any food other than a raw agricultural commodity, including any raw agricultural commodity that has been subject to washing, cleaning, milling, cutting, chopping, heating, pasteurizing, blanching, cooking, canning, freezing, curing, dehydrating, mixing, packaging, or other procedures that alter the food from its natural state” (Dwyer et al. 2012).
Also note their (US Aid) definition of 'Ultra Processed Food':
Ultra-processed foodstuffs are marked by the addition of other ingredients (e.g., preservatives, flavors, nutrients, or other additives or substances, such as salt, sugars, and fats) (Dwyer et al. 2012; Martínez Steele et al. 2016; Monteiro et al. 2019).
So, if I take tomatoes, add even a minimal amount of salt and basil, and can them, that's an 'ultra processed food'. This is what the fancy San Marzano tomato sauce you buy at Whole Foods is. If you think canned tomatoes are fundamentally unhealthy in some way, I cannot help you.
0 - https://pdf.usaid.gov/pdf_docs/PA00ZH5N.pdf