ipod touch 4 Can't connect to the iTunes or App stores

Okey-dokey, I'm up for this particular challenge.

A quick online search for the app produces a page (https://apps.apple.com/us/app/itunes-store/id915061235) from which I've taken the following screenshots:

and further down that page:

And here's the full view, showing both zoomed in parts:

The following Apple article, If you can't open the App Store or iTunes Store, buy content or edit payment information – Apple Support (UK), specifically states that if you cannot connect to the store, it may be because you are using out-of-date software or hardware. I won't post any more screenshots, because our hosts don't always appreciate too many, but see the top of that page. Further into the article, it mentions both the increased security and obsolete products, and one of the links in that article takes one to another article that specifically lists the 4th generation iPod Touch as obsolete.

So, I don't know who to believe. Both answers seem credible but in the end, neither is very helpful and I still have the same issue.

(Addressing only the "issue"), there's no way around it short of replacing the iPod with a new model. If you decide to use that option, get the 7th generation Touch rather than the 6th gen one. The 6th generation iPod Touch cannot install iOS 13 or later, so you would be short-changing yourself to buy one. Sorry to be the bearer of bad news.

I believe that an iPod with that level of software can no longer connect to the store or download apps. This is a security measure.