We were there last summer and I asked this same question. It ended up raining in the 40s the whole week. We may have seen some snow flecks.... Middle of July.....
If you're doing any hiking (Skye, the highlands etc) just have real hiking shoes or normal good quality sneakers. Once we left Edinburgh, we didn't see another person dressed to look nice again. In Edinburgh, it was pretty low key and I didn't feel the need to be well dressed when we ate out. I was wearing dark grey all birds and they were fine. I wouldn't want to wear those for big hikes though.
When I do trips like this, I also always bring a pair of black flats like these, which crush into nothing in your suitcase and can be worn to a nicer dinner.
https://www.madewell.com/the-greta-ballet-flat-99107129386.html?source=googlePLA&noPopUp=true