It's only a colour change. You can treat it the same as a blue one.

You can bookmark a link to save this link via the right-click context menu.

Hello. Is there any way to save purple links on FireFox. The links turn purple when you have previously visited them, which I would like to save. When you restart or otherwise clear your cache, the links turn back to blue. Is there any way to reverse this process so all the links, that was previously purple will be returned to this condition

To keep the visit state, you need to keep the browsing history. So if you lose the visit state then this means that you are removing history.

In case you use "Clear history when Firefox closes" or otherwise clear history.

• do not clear the "Browsing history"

• Settings -> Privacy & Security
  Firefox will: "Use custom settings for history":
  [X] "Clear history when Firefox closes" -> Settings
• https://support.mozilla.org/en-US/kb/delete-browsing-search-download-history-firefox

• using "Clear history when Firefox closes" in Firefox 102+ honors exceptions and keeps cookies with an allow exception, previous versions removed all cookies
• clearing "Site settings" clears exceptions for cookies, images, pop-up windows, and software installation and exceptions for passwords and other website specific data