Does Hebrews 13:20 or 13:22 imply Paul as Author

Heb 13:22 says: “But I urge you, brethren, bear with this word of exhortation, for I have written to you briefly.” This does not seem Pauline. It sounds more like Peter and Silas in 1 Peter 5:12 “. . . I have written you briefly, exhorting and testifying that this is the true grace of God.” For that matter “the great Shepherd of the sheep” in Heb. 13:20 is more analogous to the “Chief Shepherd” of 1 Peter 5:4 than Paul’s only use of the word “shepherd” in Eph. 4:11 describing the gift of pastor teacher.