Peter isn't merely saying that Paul uses the word longsuffering frequently. He is referring to Paul's themes along these lines. And not only the theme of God's patience, but the others he has been writing about:
A. God's patience in finally fulfilling his promises (v9a): "The Lord is not slack concerning His promise, as some count slackness, but is longsuffering..."
B. God's patience in his plan of salvation (v9b), "The Lord ... is longsuffering toward us, not willing that any should perish but that all should come to repentance."
C. The coming judgment (7): "But the heavens and the earth which are now preserved by the same word, are reserved for fire until the day of judgment and perdition of ungodly men."
D. The consequent command to holiness (11): "Therefore, ... what manner of persons ought you to be in holy conduct and godliness"
The theme of God's patience in His salvation work, wherein he will both punish evil AND reward godliness at the Judgment, is great encouragement to believers to persevere in holy living. This is most certainly the theme of nearly all the Epistles of Paul (with the exception of Philemon). For example:
Romans: Ch.1 well details the wrath of God (A.) which "is being revealed from heaven against the godlessness of men…" His theme turns to the judgment of God (C.) against both Jew and Gentile in ch.2. Then in chs.3 and 4, he establishes that salvation is entirely by faith, as it was for Abraham, who "believed the Lord, and it was credited to him for righteousness". Since these words "not written for his sake alone … but also for us" [4:23], in ch.5 he says, "we also glory in tribulations, knowing that tribulation worketh patience" (or longsuffering) (B.). He comes back to these themes in ch.8, esp in v.18
For I consider that the sufferings of this present time are not worthy to be compared with the glory which shall be revealed in us. 19 For the earnest expectation of the creation eagerly waits for the revealing of the sons of God. 20 For the creation was subjected to futility, not willingly, but because of Him who subjected it in hope. (B. and D.)
From chs.9 to 11, he answers the giant question of how the Jews fit into God's great plan, despite their present rejection of the Messiah, demonstrating from the Scriptures how God has both used them, hardened them for a time, and will "graft them back into their own olive tree" in due time… (B.)
Then in ch.12, he calls on Christians to be holy, to "present our bodies a living sacrifice, holy, acceptable to God…" And he details what this means in the remainder of his letter. (D.)
The "riches of his kindness and forbearance and patience" [Ro 2:4] (A. and B.) is a theme describing the whole of God's redemptive history. Paul patiently weaves this through 16 chapters in Romans, and several of his letters.
It is also this pattern – doctrinal truths about God and his patient work in history, followed by a call to holiness – that Peter may also be referring to, not the mere word makrothumia.
Ephesians: This letter doesn't have the same degree of discussion of such themes, but some of them recur, highlighting the patience, longsuffering, ages-long plan of God, and the same resulting call to holiness:
B. God's plan from before creation: "1:4The God and Father of our Lord Jesus Christ … chose us in Him before the foundation of the world, that we should be holy and without blame before Him in love, having predestined us to adoption as sons by Jesus Christ to Himself."
B. God's plan for future ages: "2:4 But God, who is rich in mercy, because of His great love with which He loved us, 5 even when we were dead in trespasses, made us alive together with Christ (by grace you have been saved), 6 and raised us up together, and made us sit together in the heavenly places in Christ Jesus, 7 that in the ages to come He might show the exceeding riches of His grace in His kindness toward us in Christ Jesus."
D. Which behooves us to holy living: "4:1 I, therefore, the prisoner of the Lord, beseech you to walk worthy of the calling with which you were called"
Colossians: Paul touches on these themes again in this letter,
A./B. "1:21 And you, who once were alienated and enemies in your mind by wicked works, yet now He has reconciled 22 in the body of His flesh through death, to present you holy, and blameless, and above reproach in His sight— 23 if indeed you continue in the faith"
A./D. "3:1 If then you were raised with Christ, seek those things which are above, where Christ is, sitting at the right hand of God. 2 Set your mind on things above, not on things on the earth. 3 For you died, and your life is hidden with Christ in God. 4 When Christ who is our life appears, then you also will appear with Him in glory."
D. "23 And whatever you do, do it heartily, as to the Lord and not to men, 24 knowing that from the Lord you will receive the reward of the inheritance; for you serve the Lord Christ. 25 But he who does wrong will be repaid for what he has done, and there is no partiality."
D. "4:3 For this is the will of God, your sanctification: … 6 that no one should take advantage of and defraud his brother in this matter, because the Lord is the avenger of all such, as we also forewarned you and testified. 7 For God did not call us to uncleanness, but in holiness."
A. "5:2 For you yourselves know perfectly that the day of the Lord so comes as a thief in the night."
D. "5:23 Now may the God of peace Himself sanctify you completely; and may your whole spirit, soul, and body be preserved blameless at the coming of our Lord Jesus Christ.
A. "5:24 He who calls you is faithful, who also will do it."
2 Thessalonians: The whole 1st chapter is a missive on the "flaming fire and vengeance"  God has in prepare "when He comes, in that Day, to be glorified in His saints"  (A., B., C.) This continues in ch.2 in the descriptions of the great apostacy,
A. "2:11strong delusion, that they should believe the lie, 12 that they all may be condemned who did not believe the truth but had pleasure in unrighteousness."
B. "2:13 God from the beginning chose you for salvation through sanctification by the Spirit and belief in the truth"
As a matter of interpretation, to miss the gist of a man's writing by focusing too narrowly upon the words is quite an important question. The question is quite a good one, and deserves to be discussed, since it is clearly a matter of interpretation about Peter's references to Paul. I do hope the discussion will not be stifled (as a few seem to want.)