How is "corporate right" defined? I don't know that much about how corporations expressed political positions in the 20th century, but what would we call FAANG today? They're certainly corporate, but don't seem very "right". Or are they "right" by default because they're corporate?

In any case, corporations seeking policy favorable to their cause from big government tends to appear leftist in that it is similar to what the leftist on the street wants - the government engineering the society towards some outcome as a priority over protecting the liberty of the individual.

I'm trying to sort this out in my own head. I know we normally think of business as "right", but it seems that businesses transform in to leftist behavior when the government is of a size and inclination to make winners and losers.

Yes, but so what? Leftism is often supported by rich benefactors. This only looks like a gotcha if you believe that the sort of people who talk about oppression by the rich want to walk the walk. If you look at what they do rather than what they say there is no contradiction. Here are some examples.

The Guardian pays hundreds of writers to rail against capitalism and is funded by a massive trust fund based in the Cayman Islands created via the sale of Auto Trader and related magazines. US universities are filled with people writing articles suffused with anti-capitalist rhetoric, yet are often funded by endowments from rich capitalist benefactors. Tech firms donate heavily to the Democrats.

Marx railed against capital his entire life. He claimed to be fighting for the workers, yet he employed a servant and hardly worked in the sense the working classes would recognise. The rare times he had paying jobs, it was always journalism in which he was advocating for his views. He was instead supported by a constant stream of handouts and loans from his rich capitalist friend Engels, a factory owner, along with his own family. Engels invited him to visit his factory but Marx didn't take him up on it.

Taking money from rich capitalists whilst claiming to be struggling against them is very common to see, it's not a contradiction.