Confused about sold out products

Hello – Just watched Rank Math’s video on what to do with sold out products, and I am a little confused! I do understand what was presented, but we aren’t a huge company (like Apple) so was wondering what the best option for us would be, regarding how to show or not show, sold out products?

We have hundreds of sold out products that still show as “Search and Shop” which does give us errors from Google. I need to fix this, but before I start, I wanted to make sure I was making the changes correctly.

I learned that I can change the Catalog visibility to “Search only” or “Hidden” but don’t know what is best? If I change to “search only” the product will still show up in a search on our website, along with current products for sale (not the best scenario.) But if we choose “Hidden” it won’t show at all, which is ok for generic things, but if you had a good product, that could still bring in traffic, wouldn’t it be best to choose “Search only” for that reason? That way the product still has searchability by Google?

I assume that if we choose “Hidden” then we should click the Rank Math Advanced button and click the “NoIndex” button, right?

Do Hidden items need to be removed from the XML Sitemap, or is that just for sold out products, being replaced by new products?

Would appreciate some clarification on the above.

Thanks in advance.