Updates the sidebar icon colors to match the design closer

What does this MR do and why?

This MR updates the icon colors in the sidebar to match the designs closer. It uses the --gray-500 variable so it updates correctly in Dark mode too.

Screenshots or screen recordings

Profile	Project	Context Switcher

How to set up and validate locally

Follow the steps to enable the new navigation sidebar and you should see these icons immediately

MR acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

• I have evaluated the MR acceptance checklist for this MR.

Related to #406567 (closed)