iOS 12.5.4 suggests that you have a 6th generation iPod Touch, which cannot be updated to iOS 13 or later. Apple have been clear on this point.
If you run the Check for Update procedure, the reason you see the message that your iPod is up to date is because it is up to date. That is, it has the latest version of iOS for that model of iPod. Yes, there is a later version of iOS, but your iPod cannot use it, so it is "up to date - for that model".
It's always possible though, that your iPod may (and note especially, the operative word - "may") receive future updates. As has already happened with this model; there have been security updates, within the iOS 12 range, to ensure the iPod's integrity. Those updates have not introduced any new features as far as I'm aware.
I notice your use of "iPod is not recognised" and "not recognised on iTunes":
If you mean that the software update procedure is not recognised, we've covered that point. However, iTunes can still use and manage your iPod, so if iTunes is not seeing the iPod at all, then that's a different issue. In this case, click on the blue text link and have a look at this Apple article: If your computer doesn't recognize your iPhone, iPad, or iPod - Apple Support