How do Holmes and Watson end in the last story of Arthur Conan Doyle?

It's important to note that Holmes and Watson don't actually end up together in the last story by Arthur Conan Doyle. Doyle wrote four stories after the "final" story, "The Adventure of the Final Problem" (1893) where Holmes seemingly dies. These four stories, known as the "Return of Sherlock Holmes" (1905), were written due to popular demand and are considered to be canonical.

In "The Adventure of the Final Problem", Holmes fakes his death to escape the clutches of Professor Moriarty. He goes into hiding for a few years, allowing Watson to believe he's truly gone.

When Holmes returns, he picks up his life where he left off. He and Watson continue their partnership, solving mysteries and enjoying their shared friendship.

They never explicitly end their partnership or have a "final" story. While there's no final chapter in their relationship, Doyle himself ended his involvement with Holmes in 1927 with "The Adventure of the Shoscombe Old Place". He wrote several other stories featuring other characters, but never revisited Holmes after that.

Therefore, the last story by Doyle featuring Holmes and Watson is "The Adventure of the Shoscombe Old Place", where they continue their partnership with no indication of a final farewell.