Not sure what the standard is in England, but in the United States we generally wear some sort of shirt with the governing organization on it and then whatever we need to be comfortable while still looking official. Obviously, an official tracksuit/warm-up suit is acceptable. For me, I don't like to wear a full warm-up to a game unless I'm going to officiate it, but that would clearly be acceptable dress.
I was going to observe/mentor this weekend in an indoor environment (full field indoor game) before a facility issue canceled the entire slate of games. I was going to wear a USSF (our FA) long sleeved hooded t-shirt, a pair of “smart joggers” (casual pants with elastic cuffs at the bottom), and a nice pair of sneakers. If I'm outside on a hot and humid day, I'll wear shorts and not think twice about it and obviously wear some sort of hat to protect my head. Comfort comes first, then wearing some sort of identifying apparel comes next.
Yesterday, I would have been dressed somewhat similar to this (obviously without a headset).
At least in the US, standards of dress continue to become more casual. Nothing symbolizes this more than how US basketball coaches now dress much more casually than before the pandemic. Pre-pandemic, basketball coaches almost always wore suits and ties. A few would forego the ties, but jackets were mandatory. Now I'd say 75% or more of coaches wear casual attire like polo shirts, half-zip sweaters, and even sneakers.
This article shows the evolution of coach attire. For me, I really don't care how people dress as long as they look "put together". If you want to suit and boot, have at it. If you are like me and enjoy being more casual, wear that.
