The word σημεῖον (sémeion) is used in the NT in two senses (BDAG):
a sign or distinguishing mark whereby something is known, sign, token indication, eg, Luke 2:12, 2 Thess 3:17, etc.
an event that is an indication of confirmation of intervention by transcendent powers, miracle, portent, Matt 12:38, 16:1, 4, Mark 8:11, 12, 16:17, John 2:11, 18, 23, 3:2, 4:54, 6:2, 14, 26, 30, 7:31, 9:16, 10:41, 11:47, 12:18, Acts 4:16:22, 8:6, 1 Cor 1:22, Rom 15:19, Heb 2:4, 2 Cor 12:12, etc.
I would argue that is in this latter sense that σημεῖον (sémeion) is used in 1 Cor 14:22, thus we would have:
So then, tongues are for a miracle, not to those who believe but to
unbelievers; but prophecy is not for unbelievers, but for those who
believe.
That is, the spiritual gift of tongues is for the purpose of reaching unbelievers when they cannot speak the same language, not for showing off in church services. That is, if an apostle find unbelievers who do not speak the same langues, then the Spirit might elect to enable the apostle to speak their language in order to evangelize them.
This is confirmed by other statements in the same chapter of 1 Cor 14:
- V4 - but the one who prophesies edifies the church.
- V5 - I wish that all of you could speak in tongues, but I would rather have you prophesy. He who prophesies is greater than one who speaks in tongues, unless he interprets so that the church may be edified.
- V9 - So it is with you. Unless you speak intelligible words with your tongue, how will anyone know what you are saying? You will just be speaking into the air.
- V14, 15 - For if I pray in a tongue, my spirit prays, but my mind is unfruitful. What then shall I do? I will pray with my spirit, but I will also pray with my mind. I will sing with my spirit, but I will also sing with my mind.
- V19 - But in the church, I would rather speak five coherent words to instruct others than ten thousand words in a tongue.
- V23-25 - So if the whole church comes together and everyone speaks in tongues, and some who are uninstructed or some unbelievers come in, will they not say that you are out of your minds? But if an unbeliever or uninstructed person comes in while everyone is prophesying, he will be convicted and called to account by all, and the secrets of his heart will be made known. So he will fall facedown and worship God, proclaiming, “God is truly among you!”