Hey, I'm glad to hear about your interest in the Lutheran Church! Besides prayerfully considering things, I'd be glad to briefly offer where I come from and what drew me to the Lutheran Church.
I was raised Pentecostal and spent much time in charismatic and non-denominational churches. While it's my experience that many in those denominations are very sincere and passionate for our Lord, I was blown away by how clearly God's Word is proclaimed in the Lutheran Church and how rich and Christ-centric Lutheran theology is. I greatly appreciate the Lutheran understanding of Law and Gospel, of Justification and Sanctification, and of Word and Sacraments, and also, that while tradition and reason are valued, they are always governed by God's Word, which means that in Lutheran theology, holy mysteries are embraced.
I serve in the Lutheran Church now, and one part of my work is to make Lutheran theology more readily accessible, so I'm digitising older works, reformatting and expanding them a bit, and publishing them for free. If you're interested in learning more about Lutheran theology, I can recommend skimming through our Epitomy from our Lutheran Confessions (the Concordia):
The Epitome – Luco
Regarding the phrase
"I absolve you of your sins" — You're quite right — the pastor does not have the authority to forgive sins in his name. What's in mind here is John 20:19-23, which is called the Office of the Keys, which Jesus gives to His Church, whereby He commands and promises us the following:
"If you forgive the sins of any, they are forgiven them; if you withhold forgiveness from any, it is withheld."
It's comparable to Baptism, which God works through His Church. That is, it's not by the power or authority of the pastor that people are baptised, and people are not baptised in the pastor's name, but they are baptised in the name of the Father, the Son, and the Holy Spirit. So it's God's Baptism exercised by His Church, by His will, command, and power.
Many Lutheran churches like the strong language of "I forgive you" as it's intended for their comfort — that is, it's not conditional, but simply good news that the contrite can receive without doubting if it's truly for them. However, many other Lutheran churches do use a conditional language. Our own church body does, for example. There are pros and cons to both if rightly understood. I, personally, prefer a conditional public Absolution (because there may be some unrepentant congregants), but an unconditional individual Absolution (as, in this case, those who are burdened by sin are in need of God's grace — the Gospel). In our services, I like to say:
(After the public confession of sins)
"Hear then, the promise from the Holy Scriptures, which God has promised those who truly repent of their sins and in faith turn to Him for forgiveness through His son Jesus Christ, our Lord, who bled and died for our sins upon the cross:
“As far as the east is from the west, so far does He remove our transgressions from us.”
Upon your confession, I, by virtue of my office, as a called and ordained servant of the Word, announce the grace of God to all of you who truly repent — who trust only in the person and works of our Lord Jesus Christ for your salvation — I affirm His promise of forgiveness to you in the name of the Father, and of the + Son, and of the Holy Spirit.
The Lord comfort your heart by His Holy Absolution, that your joy may be full!"
Anyway, I'd be very glad to expand on any of the above if it's helpful at all! God's blessings to you!