Is baptism about a public declaration of faith?

No.

There are only 2 people required for a baptism, the baptizer and the baptizee. There is no biblical requirement that baptism be a public declaration of faith. Witnesses are not a requirement.

The baptizee should have accepted Jesus as Messiah and acknowledge their sin with the understanding that baptism brings them into the family of God and washes away their previous sin which they have repented of.

The baptizer should submerge the baptizee in water saying either, I baptize you in the name of Jesus Christ or I baptize you in the name of the Father, Son, and Holy Ghost. There is no requirement that the baptizer be clergy, but this is often the case. In fact there is no requirement that the baptizer be a believer, but if you want them to say the correct words and submerge you completely in water it is recommended.