Eggs obviously aren't UPF, no. Eggs are in group 1 of the NOVA classification system. Using things like eggs and cornflower are fine, it's the industrial emulsifiers that are the problem.

Here's a pretty good summary:

There is nothing wrong with emulsifiers per se – think egg yolk, cornflour and other unprocessed / minimally-processed ingredients that are used in cooking. It’s the category of industrially created or modified emulsifiers over which questions hang. Examples commonly used in IDP include sodium stearoyl lactylate (E481); mono- and diglycerides of fatty acids (E471); and (deep breath) diacetyl tartaric acid esters of mono- and diglycerides of fatty acids, aka DATEM (E472e).

https://www.sustainweb.org/blogs/oct23-real-bread-is-not-ultra-processed-food-upf/