Unsure of toilet supply line diameter

I need to replace the water supply hose for a toilet. The complication I'm having is that I'm not sure of the diameter on the end that connects to my shut off valve. I've tried to measure as best I can and it seems to be slightly wider than 1/2". I'm also not sure if replacement hose is needing to come with washers in order to fit properly. Since I'm unsure of the diameter I was going to order a universal hose which has adapters for different water inlet sizes. However the hose I was thinking of ordering does not seem to come with washers where my old hose has washers in both ends.

Here is end that connects to the shut off. The plastic inner hose just broke off!!

Are the chances that the end connecting to my water supply shutoff is really a standard 1/2" and I'm just not understanding the way tube/hose diameters are measured?

Are washers optional on these types of fittings or maybe more modern hoses don't need them where older ones did?

Normally I'd just take the bad hose into the store and get this sorted out in person -- but these are not normal times! That leaves me hoping I can just order the right part and get it sent to me.