Weblio is a good source for quick JP->JP dictionary stuff.
ゆかり【▽縁／所＝縁】
１ なんらかのかかわりあいやつながりのあること。因縁。「縁(えん)も—もない」「文豪—の地」「—の者を頼って上京する」
２ 血縁関係のある者。親族。縁者。
「おのが—、西東合はせて六百人ばかり」〈宇津保・藤原の君〉
３ 《「ゆかりじそ」の略》梅干と一緒に漬け込んだ紫蘇(しそ)の葉を乾燥させて粉にしたもの。飯にふりかけたりする。
I thought (in my original post this is edited from) #3 was the source, but from looking around some more I think it’s actually referring to this furikake, which is technically a brand name:
The brand describes the name here: https://www.mishima.co.jp/study/name/, which has more information about how 縁 and purple.
It sounds like they chose ゆかり because their product is purple and because they wanted to form a connection (縁) with their customers (sure).
The weblio just talking about the furikake suggests this might now be the most common association in the modern world…
It sounds like (and confirmed with some searching of “縁の色 語源”) the purple usage is specifically because of an old （～800s) poem:
紫の ひともとゆえに 武蔵野の 草はみながら
あはれとぞ見る
The idea being I guess that the emotional connection conveyed by this purple plant in a famous poem made purple the color of ゆかり (and that in turn made ゆかり the name of a brand of purple furikake)