Is it appropriate to call Paul an apostle?

Conversion of Saint Paul, Caravaggio, 1601

Strictly speaking, this is the only criterion to qualify as a member of the college of the Apostles, one of the Twelve:

₂₁ Thus one of the men who have accompanied us during all the time the Lord Jesus associated with us, ₂₂ beginning from his baptism by John until the day he was taken up from us – one of these must become a witness of his resurrection together with us.” (Acts 1:21-22)

Paul was perfectly aware that he did not qualify.

So, in the strict sense of the word, the Apostles are the Twelve chosen directly by Jesus. In the Synoptic Gospels they are all identified, with only minor differences for Luke. The list in the Gospel of John is incomplete, but not incompatible with the Synoptics, and, in any case, in the Gospel of John, Jesus himself refers to the Apostles as "the twelve" (John 6:67-71), even three times.

The only time that Paul, in his epistles, uses the expression "the twelve", is in this passage, where Paul recognizes that ultimately his preaching of Christ's Resurrection is based on the witness of "the twelve" ...

₃ For I passed on to you as of first importance what I also received – that Christ died for our sins according to the scriptures, ₄ and that he was buried, and that he was raised on the third day according to the scriptures, ₅ and that he appeared to Cephas, then to the twelve. ₆ Then he appeared to more than five hundred of the brothers and sisters at one time, most of whom are still alive, though some have fallen asleep. ₇ Then he appeared to James, then to all the apostles. ₈ Last of all, as though to one born at the wrong time, he appeared to me also.  (1 Cor 15:3-8)

... and it is "what [he] also received" from them.

It is important to notice that Paul does not use the word "disciple" (mathētēs), which is not used either in the LXX or in the Epistles of the NT, but only in the Gospels and in Acts.

Jesus ONLY instituted as Apostles Twelve people, who were his original disciples.

If we look at the Gospels and at Acts, we find only a hint of a special apparition to Cephas (Luke 24:33-34), we do not find any mention of a special apparition to James, let alone an apparition to "five hundred of the brothers [and sisters] at the same time". On the other hand, the Gospel of Luke has an extensive account of an appartition to two disciples at Emmaus (Luke 24:13-35). In the Gospel of John, the Twelve are not referred to as Apostles but as disciples (John 20). We know that they were the Twelve (actually, only Eleven, because, obviously, Judas Iscariot was not there), because we read that Thomas Dydimus, who is explicitly referred to as "one of the Twelve", refused to believe what "the other disciples" affirmed to have seen when he was absent (John 20:24-25).

One week later, the same "disciples" (again, mathētai; John 20:26-29), this time with Thomas Dydimus, saw the Resurrected Lord Jesus Christ.

In conclusion, in spite of Paul's inconsistencies, it stands to reason that the expression "the Twelve" refers to the original group of Twelve Apostles hand-picked by Jesus.