Isn’t K’tinga the later type of Klingon ship?

The three Klingon vessels that got rekt by V’Ger at the beginning of TMP were K’Tinga class ships. That was less than 20 years after this episode was set. However, the K’Tingas did remain in service well into the 24th century, likely for the same in- and out-of-universe reasons that the Excelsior class did.