a house: a building where someone lives or where something is kept
TranslatabilityPartialCertaintySettled
This is the everyday Aramaic word for a house, and in the parts of Ezra and Daniel written in Aramaic it works exactly the way the English word does. On its own it means a building. Paired with a name in the phrase "house of X," it takes its color from that name: the house of God is the temple, the house of the king is the palace, and a house of treasures or of records is a storeroom or archive.
By far its most common use in these books is the house of God, meaning the Jerusalem temple. Whole stretches of Ezra are taken up with rebuilding it, so the word appears again and again for that one building, sometimes named in full as the house of God and sometimes shortened to "this house" once the reader knows which house is meant.
The senses below are not different words but the same word pointing at different buildings. What ties them together is simple: each is a walled structure with a purpose set by whoever owns it or by what is stored inside.
Is the everyday word for a private dwelling, someone's own home.Dan 2:17Dan 6:10
Forms the fixed name of the Jerusalem sanctuary, "the house of God," the standing term Ezra uses again and again for the temple being rebuilt.Ezr 5:2Ezr 6:3Ezr 7:23
Names an ordinary building by its function, such as the archive and treasury where royal records were stored.Ezr 6:1
Both
Both name the Jerusalem temple of God, standing side by side in one breath for the same building whose vessels were carried off.Ezr 5:14Ezr 6:5
Both can designate the residence of a king, paired together for Nebuchadnezzar's own dwelling.Dan 4:4
Attaches to state buildings named for their function: a royal treasure house, an archive where official records were stored, and a banquet hall.Ezr 7:20Ezr 6:1Dan 5:10
Both
Both name the ordinary building a person lives in and returns to.Mat 9:7Dan 6:10
Both name the temple as the house of God, the place set apart for his worship.Mat 21:13Ezr 5:2
Names a household as a family unit that acts together, above all a family that comes to faith and is saved as one: the promise reaches the man "and thy house."Act 16:31Act 11:14Act 18:81Co 1:16
Stretches to a whole people or dynasty named for its ancestor, as in the house of Israel and the house of David.Mat 10:6Mat 15:24Luk 1:27Luk 1:69
Pictures the people of God as God's own household, a spiritual house being built of living stones.1Ti 3:151Pe 2:5Heb 3:6
What scholars say about bayit
The lexica treat Biblical Aramaic bayit as the ordinary noun for house or building, cognate with Hebrew bayit and with the wider Semitic term. In Ezra and Daniel its dominant referent is the Jerusalem temple in the construct phrase bet elaha, the house of God, with further construct phrases specifying a building by function: bet malka (the royal house), bet ginzayya (the treasure house), and bet siphrayya (the house of archives). There is no lexical dispute over the sense; the interpretive questions in these chapters concern the history of the temple rebuilding, not the meaning of the word.
Sources
Koehler, Baumgartner, and Stamm, HALOT, Aramaic section, s.v. בַּיִתlexicon
Brown, Driver, and Briggs, BDB, Biblical Aramaic lexicon, s.v. בַּיִתlexicon
Franz Rosenthal, A Grammar of Biblical Aramaicgrammar