The significance is stated in the last passage you reference, Titus 3:8. “… and these things I want you to affirm constantly…”

Though Timothy was not written to Titus (obviously) it makes sense to me that Paul singling these things out as “faithful sayings” is his way of reminding Timothy (and Titus) of how important these points are and why they should remember to teach them. It’d be like if you typed out a letter and you had a sentence in bold or italics to draw the reader’s attention in for emphasis.

I don’t think Paul’s reasoning for the phrase is more elaborate than that.

The significance is stated in the last passage you reference, Titus 3:8.

… and these things I want you to affirm constantly…

Though Timothy was not written to Titus (obviously) it makes sense that Paul singling these things out as “faithful sayings” is his way of reminding Timothy (and Titus) of how important these points are and why they should remember to teach them.
It’d be like if you typed out a letter and you had a sentence in bold or italics to draw the reader’s attention in for emphasis.

I don’t think Paul’s reasoning for the phrase is more elaborate than that.