Robins only eat bugs and worms as part of their raising an egg and feeding the chicks. Once the chicks can feed themselves they all switch to fruit and seeds.

That is absolutely not my experience here. My local robins eat bugs and worms all year, however, I do see them eating fruit (wild raspberries) here, when they are in season, and the fruit of some trees. I've never seen a robin eat a seed, only fruit. Robins also have multiple broods each year here. At least two, sometimes three rounds of chicks, so it's only the very end of summer that they aren't raising chicks (or having one following them around).

In many places the summer gets very dry often near end of year, and by then most of the insects are hunted out. That, along with fruit coming into season, may be one reason you're seeing this behaviour? I live beside a river and a wetland, though, so I have insects and worms all the time.

I wonder if we're talking about different robins. European ones aren't the same as North American ones, and I'm in Canada (currently in Quebec, but the same robins are in Ontario/etc too)