There's a huge diversity of pricing and regulatory schemes across the US. I think you skepticism is well placed in general, because where I live in California the price increase has been almost entirely from bad grid maintenance policies of years past but people come up with random other excuses.

However there are some examples where increased demand by one sector leads to higher prices for everyone. The PJM electricity market has a capacity market, where generators get compensated for being able to promise the ability to deliver electricity on demand. When demand goes up, prices increase in the capacity market, and those prices get charged to everyone. In the last auction, prices were sky high, which leads to higher electricity prices for everyone:

https://www.utilitydive.com/news/pjm-interconnection-capacit...

A lot of electricity markets in other places allow procurement processes where increased costs to meet demand get passed to all consumers equally. If these places were actually using IRPs that had up to date pricing, adding new capacity from renewables and storage would lower prices, but instead many utilities go with what they know, gas generators, which are in short supply and coming in at very high prices.

And the cost of the grid is high everywhere. As renewables and storage drive down electricity generation prices, the grid will come to be a larger and larger percentage of electricity costs. Interconnection is just one bit of the cost, transmission needs to be upgraded all around as overall demand grows. We've gone through a few decades of stagnant to lessening electricity demand, and utilities are hungry to do very expensive grid projects because they get a guaranteed rate of return on grid expansion in most parts of the country.