But there is more to saving faith than just believing.
True faith obeys in the Holy Spirit, which is the process of sanctification leading to holiness.
Absolutely no work is done for salvation, it is all of the Lord. (Revelation 7:10)
But we are everywhere in the NT commanded to engage in obedience by the Holy Spirit in the process of sanctification, leading to holiness.
Bible dictionary definitions disagree with your ""sanctification leads to holiness"" narrative.
Sanctification & holiness are one in the same. They are God given & can never be lost.
Vine's Expository Dictionary of New Testament Words
Holiness, Holy, Holily
[ A-1,Noun,G38, hagiasmos ]
translated holiness" in the AV of Romans 6:19, Romans 6:22; 1 Thessalonians 4:7; 1 Timothy 2:15; Hebrews 12:14, is always rendered "sanctification" in the RV. It signifies
(a) separation to God, 1 Corinthians 1:30; 2 Thessalonians 2:13; 1 Peter 1:2;
Note: The corresponding verb hagiazo denotes "to set apart to God." See HALLOW, SANCTIFY.
[ B-1,Adjective,G40, hagios ]
(a) in Scripture in its moral and spiritual significance, separated from sin and therefore consecrated to God, sacred.
(b) It is used of men and things (See below) in so far as they are devoted to God. Indeed the quality, as attributed to God, is often presented in a way which involves Divine demands upon the conduct of believers. These are called hagioi, "saints," i.e., "sanctified" or "holy" ones.
MY NOTE: The word holy in reference to a believer is synonymous with saint/righteous sanctified/set apart for a work.
When any sinner/person places their FAITH in Jesus sin atoning death, burial & resurrection.
They are Saved/Justified by a sovereign God = Judicially declared Righteous & forever free from all sins punitive punishments demanded under Mosaic law, And every believer is FREELY given (void of any personal works) the GIFT of eternal life.
Saved/justified/righteousness & sanctification/holiness are all a one time simultaneous event. When Christ baptizes the believer with His indwelling Holy Spirit, this FREE GIFT is given via Faith & not worked for/earned.
At the moment of conversion Christ claims/covers/seals the believer with His Holy Spirit of protection & freely gives the believer eternal life.
At that moment of conversion the believer is forever: Saved/justified/righteousness, it's a DONE DEAL! Sanctification/holiness are also a DONE DEAL, yet, they are also a continuing process.
You're salvation/justification sets you apart/sanctifies you for a particular Godly life's work within Christ's Body.
Acts 26:18 To open their eyes, and to turn them from darkness to light, and from the power of Satan unto God, that they may receive forgiveness of sins, and inheritance among them which are sanctified by faith that is in me.
(MY NOTE: We are set apart by the faith OF Christ & our faith in His work. Also see - Rom 3:22, Gal 2:16, 2:20, 3:22, Phil 3:9 for more on the faith OF Christ)
1 Cor 1:2 Unto the church of God which is at Corinth, to them that are sanctified in Christ Jesus, called to be saints, with all that in every place call upon the name of Jesus Christ our Lord, both theirs and ours:
1 Cor 6:11 And such were some of you: but ye are washed, but ye are sanctified, but ye are justified in the name of the Lord Jesus, and by the Spirit of our God.
(MY NOTE: Washed/saved/justified/declared righteousness/sanctified thru FAITH placed in the ALL authoritative name & work of Christ)
Heb 10:10 By the which will we are sanctified through the offering of the body of Jesus Christ once for all.
Heb 10:14 For by one offering he hath perfected for ever them that are sanctified.
(MY NOTE: Faith placed in Jesus once for all time sin atoning death & resurrection FOREVER makes us sinless & perfect)
Jud 1:1 Jude, the servant of Jesus Christ, and brother of James, to them that are sanctified by God the Father, and preserved in Jesus Christ, and called:
(MY NOTE: Believer thru FAITH & faith alone in Christ's sin atoning death, burial & resurrection are set apart/made holy & FOREVER PRESERVED by our Great God & Savior Jesus the Christ. AMEN & amen!)