Yes he chooses all who are in Christ.
But much of the biblical election is to various jobs. Like Jacob or Paul were chosen.
Here's an important verse:
"Therefore I endure all things for the sake of the elect, that they also may obtain the salvation which is in Christ Jesus with eternal glory.”
If the elect, and the elect alone, are guaranteed salvation, why the “they also”?
In Calvinism, the elect are guaranteed salvation. There is zero chance that one of God’s elect will be lost. So why would Paul say “may” obtain, clearly suggesting that they “may not”?
For Jacob My servant’s sake, And Israel My elect, I have even called you by your name; I have named you, though you have not known Me.
Isaiah 45:4 (NKJV)
O seed of Abraham His servant, You children of Jacob, His chosen ones!
Psalm 105:6 (NKJV)
We find the word “elect” 4 times in the gospels and each time Jesus is referring to the Jews (Matthew 24:22, Matthew 24:24, Matthew 24:31, Luke 18:7).
Therefore I endure all things for the sake of Israel, that they too may obtain the salvation which is in Christ Jesus with eternal glory.”
The OT is abundantly clear that Israel is the elect of God. Nothing in scripture says He ever abandoned Israel. Jesus confirms their election during His earthly ministry when speaking of His second coming in the last days. The apostle Paul states that Israel never lost their election (Romans 9:4-5, Romans 11:2, Romans 11:28, 2 Timothy 2:10). Saved or lost, they are still His chosen people. God swore He would never forsake His chosen people (1 Samuel 12:22).
Who are the elect again? Who did God choose?
"Therefore I endure all things for the sake of the elect, that they also may obtain the salvation which is in Christ Jesus with eternal glory.”
'If the elect, and the elect alone, are guaranteed salvation, why the “they also”? '
All people to be saved must believe, no one is born saved, God uses preaching for example to reach people with the message of the gospel.
People who are elect, are so from before their birth, due to foreknowledge of God.
Example the elect are chosen to be obedient, it is not that because they are obedient thay are elect.
Foreknowledge means knowledge that comes beforehand, before these people heard the gospel of their salvation, they were elected-chosen by God to believe and have the forgiveness of their sins.
1 Peter 1 NIV
1 Peter, an apostle of Jesus Christ,
To God’s elect, exiles scattered throughout the provinces of Pontus, Galatia, Cappadocia, Asia and Bithynia, 2
who have been chosen according to the foreknowledge of God the Father, through the sanctifying work of the Spirit, to be obedient to Jesus Christ and sprinkled with his blood:
Grace and peace be yours in abundance.
1 Peter 1 NKJV
1 Peter 1
1 Peter, an apostle of Jesus Christ,
To the pilgrims of the Dispersion in Pontus, Galatia, Cappadocia, Asia, and Bithynia, 2 elect according to the foreknowledge of God the Father, in sanctification of the Spirit, for obedience and sprinkling of the blood of Jesus Christ:
Grace to you and peace be multiplied.
The election is those God calls to salvation, if God calls a gentile to salvation, then they were of that group, the elect.
Not just some Jews are elect. Gentiles also may be elect.
Example of this calling, they are called as they are elect according to foreknowledge of God, and only the elect will be saved.
Romans 9
10 And not only this, but when Rebecca also had conceived by one man, even by our father Isaac 11
(for the children not yet being born, nor having done any good or evil, that the purpose of God according to election might stand, not of works but of Him who calls), 12 it was said to her, “The older shall serve the younger.” 13 As it is written, “Jacob I have loved, but Esau I have hated.”
Then about the gentiles calling, those He calls are elect gentiles
22
What if God, wanting to show
His wrath and to make His power known, endured with much longsuffering the vessels of wrath prepared for destruction, 23 and that He might make known the riches of His glory on the vessels of mercy, which He had prepared beforehand for glory,
24 even us whom He called, not of the Jews only, but also of the Gentiles?
So we see some people from every nation, will be elected to be saved, but only those whom He calls.
Now for further confirmation Acts 15, the council of the Apostles at Jerusalem, scripture says this about some particular called gentiles that the apostles recognized as called to be saved, which is why they turned to God.
Acts 15
14 Simon has declared how God at the first visited the Gentiles to take out of them a people for His name. 15 And with this the words of the prophets agree, just as it is written:
16 ‘After this I will return
And will rebuild the tabernacle of David, which has fallen down;
I will rebuild its ruins,
And I will set it up;
17 So that the rest of mankind may seek the Lord,
Even all the Gentiles who are called by My name,
Says the Lord who does all these things.’
18 “Known to God from eternity are all His works. 19 Therefore I judge that we should not trouble those from among the Gentiles who are turning to God,
V17, God's calling has moved outwards to gentile nations.
And specifically only those who are called by Him, His calling is restricted to a subset of gentiles, not all gentiles.
And we read the Lord is the one working here, he is the one doing this calling according to election.