Batteries compete with peaker plants for diurnal variance, but they can't replace peaker plants for seasonal variance. It's an interesting dynamic.

Are there peaker plants that come online for seasonal variance?

Is that a local question for Vermont, a nation question for the US, or a global question?

If the question is global, then yes, there are, although as renewable energy has increased globally so has the need for peaker plants to handle the variance in the grid, thus plants that historically has only been used for seasonal variance are now used all year round to handle weather variance. An example of that is the oil power plant in south of Sweden.

I think what he was saying is that with a peaker plant you have an extra source of power. So if you have a low wind/low irradiance period - you can rely on peaker to provide more power, but by this stage batteries are long gone.

There is a coal power plant near me which in recent years I saw it running only during winter.

Well you're probably right that this could reduce the amount of load coming from power plants during brownouts, but the article presents it as something that is going to protect against blackouts and I really can't imagine that working as a replacement for peaker plants. If you're in silicon valley or NYC you probably think of a blackout as something that happens once or twice a year for about 15 minutes but in a lot of the country blackouts are several hours or even days long and happen fairly frequently.