Would it be fair to say that the massive public deficit is the disease, and the other two (reduced taxes & interest rates) are merely symptoms, or subsets of the former?

It is certainly related to reduced taxes. There is only so much income in a given year, and it has to be divided up. I can't think of any particularly direct way that it's related to interest rates, but I might miss something.

For an example of the tax effect, in the five years 2012-2016, the aggregate tax expense divided by the aggregate earnings before tax at Berkshire was 29.50%. In the five years 2019-2023 the same figure was 19.11%. So, as a result of the TCJA, based on the rather simple notion that all equity value ultimately comes from net earnings, a share of Berkshire is worth 14.74% more because of that one tax change. Lower taxes led directly to higher government sector deficits and higher corporate profits. It's good to be capitalists lately. Howver, I think the same can happen simply from more government borrowing. If the government is borrowing, that's because they're spending that money. A lot of that expenditure goes to companies, and less intuitively, essentially all of it shows up as corporate profits indirectly, within rounding error.

There are lots of different ways of looking at macro identities, and each way usually has an interesting implication. Often both counterintuitive and irrefutable. For example, anyone whining about current account deficits is simultaneously whining about capital account surpluses.

The identity that I referred to which addresses government sector deficits versus corporate profits has a nice write-up here:
blog.variantperception.com - Understanding the kalecki levy corporate
I like the way it starts simply then walks you through the elaborations. But it expresses an odd viewpoint, that the government sector's chosen account balance is the motive factor driving profit levels. Changes in household savings have the same effect, but isn't as big.

Jim