'The potter' being in the house of the Lord is not as strange as it may seem. Men of many different trades could be in the temple at any given time, whether offering their sacrifices or for other reasons.
12 Then Jesus went into the temple of God and drove out all those who bought and sold in the temple, and overturned the tables of the money changers and the seats of those who sold doves. 13 And He said to them, “It is written, ‘My house shall be called a house of prayer,’ but you have made it a ‘den of thieves.’”
14 Then the blind and the lame came to Him in the temple, and He healed them. 15 But when the chief priests and scribes saw the wonderful things that He did, and the children crying out in the temple and saying, “Hosanna to the Son of David!” they were indignant.... -Matthew 21:12-15 (NKJV)
Note that several different types of people are mentioned being in the temple:
- Jesus (along with His disciples, John 2:17)
- those who bought and sold
- money changers
- the blind and lame
- the chief priests and scribes
Jesus' disciples included fishermen: Peter & Andrew, James & John (Matt. 4:18-22); and a tax collector: Matthew (Matt. 9:9), all of which were in the temple at this time. So a potter being in the house of the Lord would be no more unusual than a fisherman or some other type of tradesman.
The Lord tells Zechariah to throw the 30 pieces of silver to the potter as a foreshadowing of Jesus' betrayal by Judas, who, in Matthew 27:1-10, throws 30 pieces of silver down in the temple (v5), which the chief priests use to buy a field from a potter (v7). John Gill notes that the field was
a field of no great value, or it could not have been bought so near Jerusalem for so small a sum as thirty pieces of silver. Grotius's conjecture seems to be a good one, that it was a field the potter had dug up for his use, and had made the most of it; so that it was good for nothing, but for the purpose for which these men bought it, "to bury strangers in"....
Response to question update: Concerning potter versus treasury, I side with potter (יוֹצֵר) because the only real reason for putting treasury (אוֹצָר) is if you thought יוצר was spelled incorrectly and should have been אוצר instead. I have purposely left off the vowel pointings for the previous two words to show just how similarly they are spelled, differing by only the first letter (the Hebrew was originally written unpointed).
- יצר means to form or fashion, with יוצר meaning 'one who forms.' See John Parkhurst's definition below:

- אצר means to store or treasure up, with אוצר meaning 'a treasury or storehouse.' See John Parkhurst's definition below:

Gesenius also brings this out in his lexicon (note that the words enclosed in brackets [ ] were added by the translator, Samuel Prideaux Tregelles):

The above entry says to see page CCCXLIII (343) for his entry for יוֹצֵר concerning Zechariah 11:13 (again, note that the words enclosed in brackets [ ] were added by the translator, Samuel Prideaux Tregelles):

I have also included Gesenius' entry for אׇצַר below:

I am of the same mindset as Samuel Tregelles in that the New Testament contains the true meanings of the Old Testament words and phrases. Additionally, there are many other places where יוצר is without question referring to a potter, such as:
- Psalm 2:9
- בשבט ברזל ככלי יוצר תנפצם
- Thou shalt break them with a rod of iron; thou shalt dash them in pieces like a potter's vessel. -KJV
- Isaiah 41:25
- העירותי מצפון ויאת ממזרח שמש יקרא בשמי ויבא סגנים כמו חמר וכמו יוצר ירמס טיט
- I have raised up one from the north, and he shall come: from the rising of the sun shall he call upon my name: and he shall come upon princes as upon morter [mortar], and as the potter treadeth clay. -KJV
- Jeremiah 18:2 (et al v3-6, where it speaks of the potter working with clay)
- קום וירדת בית היוצר ושמה אשמיעך את דברי
- Arise, and go down to the potter's house, and there I will cause thee to hear my words. -KJV
- Lamentations 4:2
- בני ציון היקרים המסלאים בפז איכה נחשבו לנבלי־חרש מעשה ידי יוצר
- The precious sons of Zion, comparable to fine gold, how are they esteemed as earthen pitchers, the work of the hands of the potter! -KJV
Translating יוצר as treasury in Zechariah 11:13 is more of an interpretative attempt at reconciling the obvious strangeness of a potter being in the house of the Lord. A potter being in this sequence of events does seem somewhat out of place and cryptic, but only because it foreshadowed the future event of Judas betraying Jesus for 30 pieces of silver, which wouldn't have been understood until after it occurred.