Behold, the days come, saith the LORD, that I will make a new covenant with the house of Israel, and with the house of Judah: 32Not according to the covenant that I made with their fathers in the day that I took them by the hand to bring them out of the land of Egypt; which my covenant they brake, although I was an husband unto them, saith the LORD: 33But this shall be the covenant that I will make with the house of Israel; After those days, saith the LORD, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people. 34And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more.
Both were originally given to Israel, but both apply to the church in the intermediate period.
I will sprinkle clean water on you is Priestly technical terminology , saying I will make you ritually clean again and fit to come before me. Hebrews 10 refers to the same cleansing. The Gospel is the water that washed (Eph 5:26)
The context of John 3 does appear to be baptism.
22 After these things Jesus and His disciples came into the land of Judea, and there He remained with them and baptized.
The, ‘these things’, are Jesus discussion with Nicodemus.
I read Eph 5:26 to refer directly to babtism. It is by obeying the Gospel, which calls for baptism, that Eph is refering to. Water is very important in God's plan. It is in the beginning to Christ's Death.
Gen 1 And the Spirit of God was hovering over the face of the waters.
Israel is saved by passing through the waters of the Red Sea.
Israel enters the promised land by passing through the water of the Jordan River.
Jesus was baptized:
John 1
31 I did not know Him; but that He should be revealed to Israel, therefore I came baptizing with water.”
32 And John bore witness, saying, “I saw the Spirit descending from heaven like a dove, and He remained upon Him. 33 I did not know Him, but He who sent me to baptize with water said to me, ‘Upon whom you see the Spirit descending, and remaining on Him, this is He who baptizes with the Holy Spirit.’ 34 And I have seen and testified that this is the Son of God.”
John 19
34 But one of the soldiers pierced His side with a spear, and immediately blood and water came out. 35 And he who has seen has testified, and his testimony is true; and he knows that he is telling the truth, so that you may believe.
1 John 5
6 This is He who came by water and blood—Jesus Christ; not only by water, but by water and blood. And it is the Spirit who bears witness, because the Spirit is truth. 7 For there are three that bear witness in heaven: the Father, the Word, and the Holy Spirit; and these three are one. 8 And there are three that bear witness on earth:[b] the Spirit, the water, and the blood; and these three agree as one.
Eph 5
25 Husbands, love your wives, just as Christ also loved the church and gave Himself for her, 26 that He might sanctify and cleanse her with the washing of water by the word, 27 that He might present her to Himself a glorious church, not having spot or wrinkle or any such thing, but that she should be holy and without blemish.
Makes sense to me.