What are its commonalities with Descartes' 'Cogito, ergo sum'?

The most fundamental commonality between the two is that they both seek an absolutely reliable, unquestionable "starting point" or "origin."

You can understand it this way:

Descartes pondered at the time: How do we know that everything we perceive is real? What if we are dreaming? What if an evil demon is deceiving us? He doubted everything and found that almost nothing was absolutely reliable.

But then he had an epiphany: Even if I doubt everything, even if I am deceived, the very act of "I am doubting," "I am thinking" cannot itself be doubted. As long as I am thinking, then this "thinking me" must necessarily exist.

"Cogito, ergo sum" (I think, therefore I am) became the first foundation of his philosophical edifice, an absolutely stable starting point from which all other things could be deduced. He found a "first principle" that could no longer be broken down or questioned.

And what we now commonly refer to as "first-principles thinking" is actually doing the same thing, just with a broader scope of application.

For example, if someone wants to build a car, they can approach it in two ways:

1. Analogical Thinking: They look at how others build cars and observe: "Oh, it has an engine, four wheels, and a body." Then they try to make these components a bit better or cheaper. This is how most of us approach problems, optimizing within the boundaries set by others.
2. First-Principles Thinking: They would ask, "What is the essence of a 'car'?" It's a tool to move people from point A to point B. To achieve this essence, must it have an engine and four wheels? Not necessarily. What are its fundamental constituent elements? They are the power to enable movement, the structure to support weight, the system to control direction, and so on. These most basic physical laws and requirements are the "first principles" of building a car. Starting from these origins, you might conceive of building an electric car, or even something entirely new like a "teleporter."

So you see, the core spirit of both is exactly the same:

Not being content with accepting ready-made conclusions or common sense given by others, but rather peeling back the problem layer by layer, like an onion, until you find the most core, most fundamental, unquestionable truth (the origin/starting point), and then, starting from this truth, rebuilding your understanding and solutions.

One seeks the origin of "existence" in philosophy, while the other seeks the origin of a "problem" in reality. Both are a way of thinking that involves "going back to basics and starting from scratch."