Question about site structure. NoIndex Expired Listings?

I run an e-commerce site that is more of an ebay like structure rather than your traditional e-commerce site. Essentially each product for sale is an individual listing with 1 quantity. The site structure is as follows:

Homepage > Category > Individual Product Listings

When a product sells we "archive" it meaning it is removed from the Category page but is still accessible through the direct URL with all the original product details with a message saying this is sold, please browse our category page for more products like this etc. Should I noindex these archived product listings or completely remove them from the website? Or keep as is?

My concern is that Google indexed these products and is spending resources crawling these "dead" pages so to speak.

Redirect 404 pages to Homepage. Let Google crawl it, no problem.

It's not a 404 page as all the text/images are still on the page. It's just not able to be added to the cart and has a "sold out" message.

We were told years ago by the SEO company we hired to keep these pages as they are extra pages/content for the site. Just thinking that is a bad practice.

You are better off either removing an expired product page (no point retaining a sold product page) or marking it as noindex nofollow using meta robots tag. More than worrying about Google crawling such pages and retaining them in the index, you should be really concerned about the implications of it. If Google decides to rank it on the SERPs, it would be a frustrating experience for visitors landing on the page to find it sold.

Archiving it is going to create severe content duplication problems in case you are going to list a similar product in future.