Are they coming from specific websites or are they from Firefox itself?

What "full privacy settings" have you enabled in Firefox that will stop Firefox from saving cookies?

I have strict privacy settings except for deleting cookies on closing my browser, because this makes me have to sign in to sites every time I access them. I only noticed that there were so many when McAfee offered to clean my computer. I do not know where the individual cookies came from, but if Firefox is supposed to be blocking these, why are they on my computer?

Firefox doesn't necessarily block every cookie that a website tries to save to your computer. As it sounds like you already know, cookies do actually serve a legitimate function (like keeping you logged in). Firefox tries to focus on blocking Cross-Site Tracking Cookies, which are often used for tracking (especially for ads).

Generally, the cookies that come from the website that you are visiting are fine and are serving a legitimate purpose. It's the cross-site cookies (the ones from another website) that are the issue. Blocking all cookies entirely often breaks functionality of the websites.

Depending on how many websites you use, it's not necessarily uncommon to see a large number of cookies stored in Firefox.

If you go to the about:protections page in Firefox, you can see an overview of exactly what Firefox is blocking. If you go to the Cookies and Site Data section of the Firefox settings and press the Manage Data... button, you can see a full list of what websites the cookies came from.