None of those verses actually mandate the Calvinist theory of eternal security.
Eph 1:13-14
The seal of the Holy Spirit is God's guarantee to believers - it doesn't force believers to remain in the covenant contract, but rather shows God's ownership, His guarantee of promises to those remaining in the contract, and protection from outside tampering.
What is the seal of the Holy Spirit?
The Holy Spirit as earnest payment (like a down payment or engagement ring) is also not a guarantee that someone who begins in faith will end in faith. Just like a women can reject an engagement she agreed to (but have to return the ring), the earnest payment is God's guarantee that the rest of the payment will be given in future. However, the caveat in the passage is that this future payment is only due to 'God's possession.' If someone exits the contract by rejecting faith, he can't claim the redemption of the rest of the promises in future. It's somewhat similar to how Esau could not reclaim his birthright once he had sold it, or how a woman can't claim the future benefits of marriage if she rejects the engagement she once accepted. The earnest payment is a sign of God's faithfulness to us - not a mandate of our faithfulness to Him.
Can a Christian 'give back' salvation?
24 But this man, because he continueth ever, hath an unchangeable priesthood.
25 Wherefore he is able also to save them to the uttermost that come unto God by him, seeing he ever liveth to make intercession for them. - Hebrews 7:24-25
This verse, in context, is about how Christ is able to completely save those who come to Him, unlike an animal sacrifice that could never fully atone for sins or the mortal High priests who had to annually come before God.
"For the law appoints as high priests men in all their weakness; but the oath, which came after the law, appointed the Son, who has been made perfect forever." Heb 7:28
Also, note that this forever salvation is not for those who drew near at one point in the past, but those who draw near as an ongoing action in the present. This fits well with the verb tenses of John 3:16 as well. Those who believe (continuously) are the ones who hold (continuously) salvation. Salvation begins from the first moment of faith, we continue to hold it as we continue in faith, and salvation is finally fulfilled with all the promises of God at the future judgment for those who end in faith. Jesus has no lack of ability to save or raise believers, and He is the perfect High priest.
It is only God's will that Christ raises, in future, those who look (Continuously) and believe (Continuously) in Christ. Jn 6:38-40.
What does it mean that Jesus is the author and perfecter of our faith?
I John 1:1-2 is about Jesus as the intercessor for believers who sin, and about how He is the propitiation (atoning sacrifice) for everyone's sins. Those who reject faith are not just sinning - they are returning to slavery to sin and rejecting Christ as their intercessor. (II Pet 2:20-22, Heb 10:26, etc.)
What does the Hebrews 10:26 mean concerning 'willful sin?'
2 Timothy 2:13 also does not teach eternal security. Indeed II Tim 2:12 shows quite the opposite.
"Here is a trustworthy saying:
If we died with him,
we will also live with him;
if we endure,
we will also reign with him.
If we disown him,
he will also disown us;
if we are faithless,
he remains faithful,
for he cannot disown himself." II Tim 2:11-13
Verse twelve says that "if we endure, we will also reign", but "if we deny Him He will deny us."
If someone begins in faith, but later repudiates that faith, they will be denied as if Christ 'never knew them' before the Father. It is only those who endure in faith who will reign with Him.
In verse 13, the verse speaks of God's faithfulness. What faithfulness? To His own self and character. God 'can not deny Himself' - even if an unbeliever or former believer has unbelief, that doesn't change God's promises nor who He is. As such, God *cannot* break His own promises and raise an unbeliever, for that would be denying His own promises and character.
"Being confident of this very thing, that
he which hath begun a good work in you will perform it until the day of Jesus Christ..." - Philippians 1:6
Paul is praising the Philippians for their active participation in the gospel, and expressing his own personal confidence that God will continue working in them. The 'good work' in us is the work of the Spirit in renewing our mind and helping us put to death the deeds of the flesh as we walk in Christ, and the equipping of the believer by the Spirit for every good work (II Tim 3:17.)
We get more explanation from Phil 2:13 "Therefore, my beloved, just as you have always obeyed, not only in my presence, but now even more in my absence,
continue to work out your salvation with fear and trembling, or it is God who is at work in you, both to will and to work for His good pleasure."
And in Col 1:9-14: "For this reason, since the day we heard about you, we have not stopped praying for you.
We continually ask God to fill you with the knowledge of his will through all the wisdom and understanding that the Spirit gives, so that you may live a life worthy of the Lord and please him in every way: bearing fruit in every good work, growing in the knowledge of God,
being strengthened with all power according to his glorious might so that you may have great endurance and patience, and giving joyful thanks to the Father, who has qualified you
f to share in the inheritance of his holy people in the kingdom of light. For he has rescued us from the dominion of darkness and brought us into the kingdom of the Son he loves, in whom we have redemption, the forgiveness of sins."
II Tim 2:20-21, II PEt 1:3-11, II Cor 4:7-18, and many other passages speak to this work of God inside us as well.
Etc. These passages are about God equipping us for every good work, His Spirit working in believers until the day of redemption. None of them are about God forcing us to continue in faith, forcing us to submit to Him, etc. That God equips us as we walk with Him and gives us everything we need for life, godliness, growth, endurance, etc. doesn't logically mandate that we continue to walk with Him. It does mean that those who reject faith have no excuse - they can't claim God did not give them what they needed or do enough for them.
None of those passages mandate eternal security, nor do they contradict the many explicit scripture passages that speak of individuals falling away/rejecting faith, the possibility that believers can fail to endure in faith, the warnings that we need to hold fast in faith, etc.
What is the underlying Greek word used for translating "falling away" in the NKJV & "departure" in the WEB?
What is 'perseverance of the saints' and is it biblical?
Does Hebrews 6:4-6 mean we can lose our salvation?