What do we have to say about Sahih Muslim Hadith 4577 in which Hazrat Abbas (RA) uses harsh words against Moula Ali (AS) calling him a liar, sinner, covenant-breaker, and traitor?
There is big misunderstanding in your quoting of the Hadeeth in Salih Muslim. The Hadeeth is narrated from Malik ibn Aws مالك بن أوس from Omar ibn Al-Khattab that Omar told Abdullah Ibn Abbas that you and your cousin Ali Ibn Abi Talib looked at Abu Bakr and at me as liars, sinners, covenant-breaker and traitor. (Salih Muslim, 5;152).
'Omar was telling Abdullah Ibn Abbas what he and Ali (AS) thought about Abu Bakr and Omar.
This Hadeeth was narrated also in Musannaf Abdul Razzaq 5;472.
Bukhari has also narrated this Hadeeth from Musannaf Abdul Razzaq but he omitted two words from it.
Wassalam.