There are, indeed, differences between the first account of creation in Genesis, and the second account in Genesis. The second account commences with chapter 2 verse 4. The points you raise may be due to the arrangement of words in the Septuagint version being followed too slavishly. The correct words are then set in the wrong place, resulting in an unintelligible contradiction. More on that later.
First, the real significance of the two accounts:
"In the opening chapters of Genesis what immediately strikes the eye is the way in which the record of the Creation is repeated. There is not just one account. There are two accounts of Creation. These differ in length, content, and emphasis. This in itself indicates a profound mystery. Yet a mystery rarely noticed, seldom considered, and hardly opened.
The first account of Creation begins at Genesis 1:1 and ends at 2:3. These verses are characterized by the name ELOHIM - translated GOD in the English Bible - used exclusively in this passage and occurring thirty-three times.
The remainder of chapter two - that is, verses 4 to 25 - presents the second record of the Creation. This is worded in a completely different manner and considered from an entirely distinct aspect. Throughout this passage the divine name Elohim is marked by the addition of the name JEHOVAH, so as to read Jehovah Elohim, translated LORD God in the English Bible. This name occurs eleven times in these verses." Creation, John Metcalfe, pp.64-65, fifth impression 2008, http://www.johnmetcalfepublishingtrust.co.uk/contact_us.htm
Notice needs to be taken of such things as why the first account makes no mention of Adam, or even the ground (Adamah), nor the fact that the man was to be a living soul. Eden is not mentioned, nor the trees of life and of the knowledge of good and evil. But the second account is concerned to introduce the man by name - Adam - and goes on at length about him, his manhood, his history and his posterity. He can then be seen as the head of the fallen race.
As the covenant name of God is only introduced on the seventh day, so did God only bring his covenant name to his people, Israel, via Moses. They had the first volume of the Torah - Genesis - and could now go back in time behind Jacob, Isaac and Abraham, to find their ultimate origin and root in Adam under the divine name Jehovah Elohim. Genesis 2:4 shows the beginning of the revelation of Jehovah to Israel, made known in Adam.
Therefore, without grasping the two accounts of Creation, and their deliberate use of certain words and avoidance of other words, there will be confusion. A strictly literal translation of Gen. 2:5 gives, "And every bush of the field not yet was it in the earth; and every green herb of the field not yet was it sprung up." (John Metcalfe, Ibid. p. 68) Also, "And no shrub of the field is yet in the earth, and no herb of the field yet sprouteth, for Jehovah God hath not rained upon the earth, and a man there is not to serve the ground" (Young's Literal Translation). And also, "And no plant of the field was yet in the earth, and no herb of the field had yet sprung up. (Revised Version)
If the word 'before' is brought to the front of the clause, and then the word 'it' is dropped, the verse now reads, "And before any plant of the field was in the earth, and before every herb of the field grew". This makes sense in view of verse 4:
"Observe the wording of verse 4 again: 'These are the generations of the heavens and of the earth when they
were created, in the day that Jehovah Elohim made the earth and the
heavens.' Now, that day was the first day, Genesis 1:1. But - again note the translators' comma at the end of 2:4 - Genesis 2:5 continues to speak of the condition of things - described in Genesis 1:2 as being without form and void - on that same day. That is, the first day. three days before any plant was in the earth, and before any herb of the field grew. It was the first day of Creation, Genesis 1:1-5. Of this day, Genesis 2:4-5 speaks. Not until the third day - Genesis 1:9-13 - did vegetation appear on the earth.
To summarize: the words 'in the day' - Genesis 2:4-5 - correspond with
the first day of Genesis 1:1-5." (Ibid. pp. 68-69)
More is explained by the author to show that the earth was clothed with verdure on the third day, whereas man was not created until the sixth day. As to rain, this did not fall until the Flood, so lack of rain and the absence of man could not be the reason for lack of verdure. On this point he concludes:
"Because of the difference in the viewpoint of the narrative, Chapter
1:1 to 2:3 states the events that took place in seven days, and the
view of man on the sixth day uses the narrative of those events so as
to point to and foreshadow a Man and a Creation yet to come.
Not so chapter 2:4-5. Creation is briefly mentioned, but here the
first man Adam is the subject of the narrative. The Creation awaited
his being formed, to reach the fulfilment of its purpose Israel, chosen of Jehovah, should consider his origins, and ponder that
purpose." (Ibid. p. 70)