I think now that what Jesus means by “water” when He talks about His baptism, is the Holy Spirit.
Jeremiah 2:13 - [Thus says the LORD] "For My people have committed two evils: They have forsaken Me, the fountain of living waters, to hew for themselves cisterns, broken cisterns that can hold no water."
Jeremiah 17:13 - "O LORD, the hope of Israel, all who forsake You will be put to shame. Those who turn away on earth will be written down, because they have forsaken the fountain of living water, even the LORD."
My comment: Where the English says "LORD", the Hebrew says "YVWH" [often transliterated "Yahweh"], which Jews often--if not always--replace with "HaShem" ["The Name"].
John 4
4 Now [Jesus] had to go through Samaria.
5 So he came to a town in Samaria called Sychar, near the plot of ground Jacob had given to his son Joseph.
6 Jacob’s well was there, and Jesus, tired as he was from the journey, sat down by the well. It was about noon.
7 When a Samaritan woman came to draw water, Jesus said to her, “Will you give me a drink?”
8 (His disciples had gone into the town to buy food.)
9 The Samaritan woman said to him, “You are a Jew and I am a Samaritan woman. How can you ask me for a drink?” (For Jews do not associate with Samaritans.
10 Jesus answered her, “If you knew the gift of God and who it is that asks you for a drink, you would have asked him and he would have given you
living water.”
11 “Sir,” the woman said, “you have nothing to draw with and the well is deep.
Where can you get this living water?
12 Are you greater than our father Jacob, who gave us the well and drank from it himself, as did also his sons and his livestock?”
13 Jesus answered, “Everyone who drinks this water will be thirsty again,
14
but whoever drinks the water I give them will never thirst. Indeed, the water I give them will become in them a spring of water welling up to eternal life.”
15 The woman said to him, “Sir, give me this water so that I won’t get thirsty and have to keep coming here to draw water.”
Revelation 7
9 After these things I looked, and behold, a great multitude which no one could count, from every nation and
all tribes and peoples and tongues, standing before the throne and before the Lamb, clothed in white robes, and palm branches
were in their hands;
10 and they cry out with a loud voice, saying, “Salvation to our God who sits on the throne, and to the Lamb.”
11 And all the angels were standing around the throne and
around the elders and the four living creatures; and they fell on their faces before the throne and worshiped God,
12 saying, “Amen, blessing and glory and wisdom and thanksgiving and honor and power and might,
be to our God forever and ever. Amen.”
13 Then one of the elders answered, saying to me, “These who are clothed in the white robes, who are they, and where have they come from?”
14 I said to him, “My lord, you know.” And he said to me, “These are the ones who come out of the great tribulation, and they have washed their robes and made them white in the blood of the Lamb.
15 “For this reason, they are before the throne of God; and they serve Him day and night in His temple; and He who sits on the throne will spread His tabernacle over them.
16 “They will hunger no longer, nor thirst anymore; nor will the sun beat down on them, nor any heat;
17 for
the Lamb in the center of the throne will be their shepherd, and will guide them to springs of the water of life; and God will wipe every tear from their eyes.”
Revelation 21
5 And He who sits on the throne said, “Behold, I am making all things new.” And He said, “Write, for these words are faithful and true.”
6 Then He said to me, “It is done. I am the Alpha and the Omega, the beginning and the end.
I will give to the one who thirsts from the spring of the water of life without cost.
Revelation 22
1 Then the angel showed me
the river of the water of life, as clear as crystal, flowing from the throne of God and of the Lamb
2 down the middle of the great street of the city.
My comment: I was taught early in life that "living water" refers to "flowing/running water" as opposed to standing water in a well or lake.