Why can I be positive that apostle Paul, in Titus 3:5, is talking about baptism? He doesn't use the word "baptism" here. Couldn't someone argue that it's just a metaphor for the work of the Holy Spirit? — R.R.

Yes, someone could try to see a metaphor here, and in many other passages. But the understanding of most scholars and of the early church is that the washing in Titus 3:5 is the washing of John 3:5—in baptism. Let's look at the broader

baptism line drawing emersion - World Wide Wolfmueller
At one time we too were foolish, disobedient, deceived and enslaved by all kinds of passions and pleasures. We lived in malice and envy, being hated and hating one another.
 But when the kindness and love of God our Savior appeared, he saved us, not because of righteous things we had done, but because of his mercy. He saved us through the washing of rebirth and renewal by the Holy Spirit, whom he poured out on us generously through Jesus Christ our Savior, so that, having been justified by his grace, we might become heirs having the hope of eternal life (Titus 3:3-7).

The description speaks of baptism. The point is elaborated here, along with other references: https://www.douglasjacoby.com/titus-3/.

Hope this helps!