> "over-building so you have enough in winter" This makes wind and solar much more expensive to the point where nuclear is cheaper.

No it doesn't. Why do you just say that? There are simulation studies like CSIRO's work which show that it's still cheaper than nuclear after you account for everything.

> But not in grid storage. That is still incredibly expensive.

The price of grid storage is absolutely falling exponentially with respect to time.

Please provide proof

See the first graph on this page for example: https://ourworldindata.org/battery-price-decline

I will admit you are right when someone installs a grid scale battery with 7 days of storage at at least 100MW of output

Batteries are only one of many inputs needed for grid storage.

Batteries utterly dominate the cost of grid storage... everything else is a rounding error.

You're welcome to go find your own data of course, you'll struggle to find more direct numbers because significant grid storage has only become affordable in the last few years.