You have done a very careful analysis.
bara does not mean "create out of nothing" as @A. Meshu has said.
We know this because God created man using the dust of the earth.
bara means to create something new that has not existed before.
You left out verse 1.
In the beginning, God created the heavens and the earth.
This uses the word bara.
This is not a title as some think because the next verse starts with "and".
In the beginning God created the universe out of nothing.
We then see following v1, on days 1-6 that God did not create anything out of nothing.
It was all there from v1.
How long ago was that? The Bible doesn't say. It was in the beginning.
Day 1: Neither עשה nor ברא is used in describing creation of the light, but instead we have yehi owr wa-yehi owr ('Light shalt exist.' And light existed.)
God didn't create or make light here because light already existed.
God had created it in v1 as part of the universe.
How can God create a universe without light?
Are we to believe that God created water, fire, heat, sound, and all the elements in v1, but not light?
v2 says darkness was upon the face of the deep.
This implies there was light elsewhere in the universe.
It is like if I said, there was darkness over my whole neighborhood.
That implies that outside my neighborhood somewhere, there was light.
If the entire universe was dark, why would God say, Darkness was on the face of the deep?
When God said, let there be light, He brought light to the earth.
This was when the first of the 7 days began.
This was 6,000 - 8,000 years ago.
I understand that most Christians think the first of the 7 days began with v1.
The text does not say when this day began.
But it tells us when the this and all the days ended.
They all ended at the morning of the next day
Gen 1:5 And God called the light Day, and the darkness he called Night. And there was evening, and there was morning -- one day.
H.C. Leupold says it better than I could:
"Then came evening, then came morning - the first day." To try to make this mean that the day began with evening, as days did according to the later Jewish reckoning (Lev 23:32), fails utterly, because verse 5 reports the conclusion of this day's work not its beginning. - H. C. Leupold
Day 2: עשה is used to describe creation of the firmament
God made the firmament around the earth. God had already created firmaments in v1, so God was not creating something that never existed before.
Now He made one for the earth.
The firmament is the earth's atmosphere which keeps the clouds separated from the earth, so we can see.
The firmament of the heavens, (definite article) into which God placed the stars on the 4th day, is our galaxy, which God created when He created the heavens in v1.
I never thought of the firmament being the galaxy before, but I think it makes more sense than any other interpretation I've ever heard! - Pascal's Wager
Thanks! I say that because God set the stars in the firmament.
Day 3: Neither verb is used for God's creation of plants, but instead the earth "sprouts" (דשא) the vegetation. The verb עשה, however, is used to describe the tree "bearing" fruit (perhaps, in its own way, "creating" fruit?)
I think the plant seeds were already left there from a previous creation on the earth that got destroyed between v1 and v2.
Day 4: עשה is used to describe creation of the luminaries
God had already created the heavens in v1. That includes the stars.
Here God made the stars in our galaxy.
He uses the verb "made" because stars already had been created in v1, so God was not creating something that never existed before.
There were stars in other galaxies, but not in our galaxy.
All the stars visible to the naked eye are in our galaxy. The closest galaxy to our own, Andromeda, looks like 1 star.
Day 5: ברא is used to describe creation of the sea-animals and sky-animals
These are new creatures, so God created them.
Day 6: עשה is used to describe creation of the land-animals. עשה is also used when God says, "Let us create man in our image." But then, we have ברא used 3 times when God says "So God created man in his own image, in the image of God created he him; male and female created he them."
Man was something new that never existed before.
From what you wrote, it sounds like ברא is used when God makes something for the first time ever and עשה is used when he makes something that has already been made before. – Pascal's Wager
Yes, and this is illustrated by the verse that summarizes all God's creation work in chapter 1:
Genesis 2:3 And God blessed the seventh day, and hallowed it, because that on it he rested from all his work which God created for making.
"created for making" is what the Hebrew literally says. Or it could be translated "created [in order] to make".