Paul is quite specific as to how sin entered our own sphere of existence :
... by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned: [Romans 5:12, KJV.]
In this particular place he attributes the entrance of sin, into our own realm, to one man. The text you quote in I Timothy enlarges on that and conveys the role played by woman.
The writer to the Hebrews conveys three things about the nature of angels :
And of the angels he saith, Who maketh his angels spirits, and his ministers a flame of fire. [Hebrews 1:7, KJV.]
Firstly, as to their being, they are spirit-beings, that is to say, they have no personal material or substantive form as we humans do. It is clear from many scriptures that they may, as messengers (which is what both the Hebrew malak and the Greek aggelos mean) take, temporarily, either a manifestation of humanity or they may appear in a dream in a form which expresses their messenger role.
Secondly, the nature of their life, the way in which their life functions (which will be different from humans whose 'life' is in their 'blood', that is to say breathed in atmosphere flowing through the bloodstream to every part of the body energises human nature). The mode of the life-function of angels is likened (so that we may understand it) to fire - a burning, non-solid, energy.
Thirdly, their existence is (as should also be the case for humans) a continual service towards God, as Gabriel made clear to Zachariah when he said :
I am Gabriel, that stand in the presence of God; and am sent to speak unto thee, and to shew thee these glad tidings. [Luke 1:19, KJV.]
The writer to the Hebrews also makes clear what the remedy is for sin, with regard to humans :
And deliver them who through fear of death were all their lifetime subject to bondage. For verily he took not on him the nature of angels; but he took on him the seed of Abraham. [Hebrews 2:15 and 16, KJV.]
Speaking of Jesus Christ, the writer makes it clear that Jesus Christ 'took on' the nature of humanity in order that humans might be redeemed from sin. By partaking of their nature and suffering on their behalf, he redeemed them from the transgression of humanity.
I can find nothing in scripture that expresses anything similar to this in regard to angels except the expression 'elect angels' :
I charge thee before God, and the Lord Jesus Christ, and the elect angels, that thou observe these things ... [I Timothy 5:21, KJV.]