First, this passage has to be read correctly as describing three kinds of trees, not four. E.g. the passage should be read as:
And on the first day you shall take
for yourselves the first fruit of hadar trees:
1. branches of palm trees
2. and branches of a leafy tree
3. and of a brook’s poplar trees,
and you shall rejoice before Yahweh
your God for seven days."
E.g. Here is the Hermeneia commentary:
The product of hadar trees: There is no positive horticultural
identification of a tree, or a type of tree, called hadar. Words
probably related etymologically to hadar connote beauty and majesty.
Hebrew ʿets hadar, “hadar trees,” is a general category that is
followed by the specification of three beautiful trees: (1) kappot
temarim, “palm branches,” (2) ʿanaf ʿets ʿavot, “branches of leafy
trees,” and (3) ʿarvei naḥal, “willows of the brook.” This greenery
symbolizes the abundance of water and oases and the beauty of the Land
of Israel. Traditionally, the “fruit of the tree” has been taken to
be the citron (ʾetrog). It is a much later addition to the Sukkot
Note that during the middle ages, jewish tradition decided that the "fruit of the tree" was an 'etrog (or citrus tree) but such trees were not native to Israel even though they were abundant in Babylon. The word 'etrog is not even of Hebrew origin, it is a loan word from Persia, which most likely entered the Hebrew lexicon during the exile. By roughly the first century AD, the citrus tree was associated with tabernacles. Then about a thousand years later, medievel jewish tradition reinterpreted the citron as being part of the original trees (since commentators such as Rashi had no way of knowing which flora was native to Israel during the iron age).
If we try to uncover what the three hadar (beautiful, majestic) trees symbolized during the time of Moses, we should look to mention of these in scripture and other ANE texts rather than medieval Spanish commentaries.
The Palm tree (tamar in Hebrew) is a date palm and has mulitple layers of symbolism.
As the desired and hated bride:
Tamar, the daughter-in-law (and wife) of Judah. Onan desired her but practiced birth control, and she tricked her father in law into sleeping with him by posing as a prostitute. Judah was about to kill her by fire when she revealed that he was the father.
Tamar, the beautiful sister of Absalom. Her brother Amnon fell in love with her, tricked her, raped her, and then hated her, whereupon Absalom killed him and many of the other sons of David.
So the idea here is that, like the righteous, who are also compared to date palms (Psalm 92.12), they are both desired (by the wise) but hated (by the wicked). This then is the fate of Israel when it dwells in the booths, living as strangers in the land, being both desired and hated as Israel is the bride of God. Specifically they are desired by the groom (Song of Solomon 7.7-8), a symbol of God but they are hated by the gentiles.
Symbolism in the tabernacle
The tabernacle is the dwelling place of God, so the symbolism here is that it is the flesh, or the body, as God dwells within us (we are the temple of God). This is lived out in Tabernacles where for seven days we are to live in booths made with date palm branches, and thus the date palm is a common motif in Solomon's and Ezekiel's temples (Eze 40.22, Eze 40.26, 1 King 6.32, 1 king 6.35). Again, symbolism an aspect of our nature, that we are the bride.
The Hebrew reads ets avot, ets just meaning tree, but avot has the connotation of a dense canopy rather than just leaves. Thus the avotim is also translated as "thick clouds" in the OT (See Eze 31.10). In other places, it is translated as "thick foliage" (Eze 31.14). For this reason, the connotation is primarily one of covering and providing shade, creating an inner place (often a secret place), for the heart. In the prophets, people commit idolatry in these secret places (Eze 6.13), but God can also dwell in the inward parts. Thus the leafy trees, in our description of the tabernacle as a type for the body or temple of God, is the inward life.
Poplar trees beside the brook
Continuing this analogy of the tabernacle as the body of the believer, we have first the palm trees that designate the bride, the thick canopy that designates the inner life happening within, and within that thick canopy is a brook! A stream of water alongside grow willows or poplar trees. The picture of the poplar tree growing next to a brook is symbolic of the new man, the inner man, dwelling within the leafy canopy.
For I will pour water upon him that is thirsty, And floods upon the
dry ground: I will pour my spirit upon thy seed, And my blessing upon
thine offspring: And they shall spring up as among the grass, As
willows by the water courses.
But, at the same time - as a warning -- the beast that does not know God can also dwell in the same place, and the beast will "drink up" the stream, devouring it:
He lieth under the shady trees, In the covert of the reed, and fens.
The shady trees cover him with their shadow; The willows of the brook
compass him about. Behold, he drinketh up a river, and hasteth not: He
trusteth that he can draw up Jordan into his mouth. [KJV]
So this again is a warning that we can have Christ in the Temple, or the antiChrist. However the stream and poplar trees are there.
 Levine, B. A. (1989). Leviticus (p. 163). Philadelphia: Jewish Publication Society.