what is the meaning of 'as recent history goes'

Not really, although time passing would certainly be a requirement. It refers to recent events that have occurred in recent history. Usually ones that you or your parents have lived to observe or experience, and the lessons we as a society have (hopefully) learned from those experiences. For example: A basketball team that had recently gone through a long stretch of losing seasons, might be expected to have another such season this year because “as recent history shows us,” that’s likely to be the case again.

While the other answer is on point, let's go just a little deeper...

If you google a bit and play a bit with the search term such as "as * history goes" (of course using the "" to make it a phrase and the * to allow for some variation), you may find that the basic pattern to this casually used expression is

as the story goes, ...

which is just an idiomatic way of saying that the part in the "..." is some content of some often-told popular story or information, usually something that is narrated - could be anecdotes, romance, fairy tales, popular accounts of fact (or what facts may remain after the account has become a popular story that people like to tell), pretty much anything that people like to tell or hear repeatedly, which is surely true with fans of team sports talking about club and team history.

So your speaker was basically using that pattern in a slight variation which here has a slightly more factual touch (of course history would rather be hard facts than not, albeit maybe distorted a bit or not if it is popular talk that could be more interested in telling the story in itself than in exact details in some places, but I digress.)

The basic information is, of course, that "Manchester was once 'red' again" but [this did] not [last] for [a] long [time] (that's the part in the position of the "..." in the pattern). If it was just told in the basic pattern, it would obviously be Manchester was once red again, as the story goes, that is, as people like to tell what happened.

In the variation, you have the added information that this is not just a story people tell but actual history, and that it is recent. So the full meaning of the sentence conveys that the state of affairs first mentioned, Manchester was red, was achieved but did not last long as we know because we know about the course of recent events that followed - there was soon a change in the "colors" that mark the time the once victorious club prevailed.

On a side note, there is also

the story goes that ...

i.e. people like to tell a story about ...

As the story goes, in the last year of his reign, King so-and-so commanded his faithful servant to saddle his horse and accompany him to...

You can find more of the kind on a number of text/translation related knowledge engines around the world. One resource I like is linguee that presents snippets from actual text found on the internet (actually, along with translation to one of several second languages to choose from - usually using translations of the same text found on the internet in the other language, but I digress.).

As for the expression as time passes, that is not the same - that is a different expression that would be used more in referring to things in the present or that you would expect in the future as they commonly are that way - as time passes, we all get older and hopefully wiser. But that might be a different question - did you have a look at the suggestions that the system might give you to look at when when you press the "Review your question" Button? Anyway, just in case you're interested, as an extra, I'll mention that you can find that expression used in this (albeit closed) question on the Worldbuilding stackexchange.