To me it looks like Joshua and co. are being told that G-d will bring His servant "Branch".
Not so related, I don't think "they are men wondered at" is a correct translation. מופת is a noun not an adjective (Deut. 13:2). So אנשי מופת means "men of a wonder (wonder being synonymous with a sign- something that causes wonderment)".
I see where you're coming from, but Zerubabel was already prophesied explicitly as the one to build the Temple in 4:9. So this verse is G-d telling the High Priest (presumably a High priest would have some vested interest in a Temple being built) that He's going to send someone to build it. I'm guessing Joshua is also being knighted here with the crowns since he along with Zerubabel are the two leaders who led the people out of Babylon.
Also, the actual translation of the word we are translating as "branch" is really "sprout" (you have this root word in Gen. 2:5 "before it had sprouted"). If Zerubabel is a contraction of "Zeru'a Bavel" or even "Zera Bavel", which mean seed/ed in Babel, then calling him the "sprout" would imply he's fulfilling a purpose directed for him.
I don't see one as having anything to do with the other. He's not sitting on the throne, he's building the Temple.
Being "seeded" in Babel - actually only means he was conceived in Babel.
"If the name
Zerubbabel is Hebrew, it may be a contraction of
Zərua' Bāvel (Hebrew: זְרוּעַ בָּבֶל), meaning "the one sown of Babylon", and referring to a child conceived and born in Babylon; or perhaps even,
Zərûy Bāvel (Hebrew: זְרוּי בָּבֶל), meaning, "the winnowed of Babylon", in the sense of being exiled in Babylon. If the name is not Hebrew but Assyrian-Babylonian, it may contract,
Zəru Bābel, meaning, "Seed of Babylon", the one conceived in Babylon. (Contrast the related Hebrew form for "Seed": Hebrew: זֶרַע,
Zera '.)"
https://en.wikipedia.org/wiki/Zerubbabel
The problem though is that they are together in these specific verses. Joshua is with Zerubbabel leading the people out of Babylon. They are together building the temple, etc. And the verse makes it appear that Joshua is being called the Branch.
Supposedly Zerubabbel was given the task of rebuilding the Temple in the second year of the reign of Darius I (520 BC), along with the high priest Joshua son of Jehozadak.
We are also told that Sheshbazzar laid the foundation stones for the temple. It is speculated that Sheshbazzar was in fact Shenazzar, Zerubabbel's uncle (mentioned in Chronicles); Sheshbazzar began the work and Zerubbabel finished it, along with Joshua.
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"Zec 4:6 Then he answered and spake unto me, saying, This
is the word of the LORD unto Zerubbabel, saying, Not by might, nor by power, but by my spirit, saith the LORD of hosts.
Zec 4:7 Who
art thou, O great mountain? before Zerubbabel
thou shalt become a plain: and he shall bring forth the headstone
thereof with shoutings,
crying, Grace, grace unto it.
Zec 4:8 Moreover the word of the LORD came unto me, saying,
Zec 4:9 The hands of Zerubbabel have laid the foundation of this house; his hands shall also finish it; and thou shalt know that the LORD of hosts hath sent me unto you.
Zec 4:10 For who hath despised the day of small things? for they shall rejoice, and shall see the plummet in the hand of Zerubbabel
with those seven; they
are the eyes of the LORD, which run to and fro through the whole earth.
Zec 4:11 Then answered I, and said unto him, What
are these two olive trees upon the right
side of the candlestick and upon the left
side thereof?
Zec 4:12 And I answered again, and said unto him, What
be these two olive branches which through the two golden pipes empty the golden
oil out of themselves?
Zec 4:13 And he answered me and said, Knowest thou not what these
be? And I said, No, my lord.
Zec 4:14 Then said he, These
are the two anointed ones, that stand by the Lord of the whole earth.
"There is a debate in the Biblical scholarly community as to who the "sons of oil" is referencing. Though conventional wisdom often understood it to be Zerubbabel and Joshua, Boda argues that, because of the important role that prophets were said to play in the reconstruction of the Temple in Zech 8:9,
Haggai and Zechariah are the sons of oil.
The controversy regarding the prophesies
about Zerubbabel relate back to this quote about Zerubbabel laying the foundation of the temple and eventually completing it. Zech 3:8 and 6:12 refer to a man called "The Branch." In Zech 6, the Lord
tells Zechariah to gather silver and gold from the returned exiles (who had come back to Judah from Babylonia), and to go to the house of Josiah son of Zephaniah (members of the Davidic lineage). Then Zechariah is told to fashion a
crown out of the silver and gold, set it on the head of Joshua son of Jehozadak, and tell him the following:
"Thus says the Lord of hosts:
Here is a man whose name is Branch (Hebrew:
Zemah): for he shall branch out in his place, and he shall build the temple of the Lord … he shall bear royal honor, and shall sit upon his throne and rule. There shall be a priest by his throne, with peaceful understanding between the two of them." (Zech 6:12–13)"
https://en.wikipedia.org/wiki/Zerubbabel
Joshua is crowned - thus sits on a throne, - and was there at the Temple build, etc.
To me the most telling though - is the fact that the two men were together often, - but there is no mention of Zerubbabel in the "naming" the Branch verse.
If he were the Branch - they would have named him - as they knew him.
Plus his line was cursed. He can't be crowned. A governor maybe.
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