Add more tests to continuous integration

Cherry-picking reasonable checks from
 https://github.com/jj-vcs/jj/blob/main/.github/workflows/ci.yml

Author: boivie

.github/workflows/ci.yml

@@ -9,6 +9,7 @@ env:
 
 jobs:
   test:
+    name: build and test
     runs-on: ubuntu-latest
     steps:
       - uses: actions/checkout@v4
@@ -18,3 +19,45 @@ jobs:
         run: cargo build --verbose
       - name: Test
         run: cargo test --verbose
+
+  check-rustfmt:
+    name: check (rustfmt)
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: dtolnay/rust-toolchain@stable
+        with:
+          toolchain: nightly
+          components: rustfmt
+      - run: cargo +nightly fmt --all -- --check
+
+  check-clippy:
+    name: check (clippy)
+    permissions:
+      checks: write
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: dtolnay/rust-toolchain@stable
+        with:
+          toolchain: stable
+          components: clippy
+      - run: cargo +stable clippy --all-features --workspace --all-targets -- -D warnings
+
+  check-doctests:
+    name: check (doctests)
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: dtolnay/rust-toolchain@stable
+      # NOTE: We need to run `cargo test --doc` separately from normal tests:
+      # - `cargo build --all-targets` specifies: "Build all targets"
+      # - `cargo test --all-targets` specifies: "Test all targets (does not include doctests)"
+      - name: Run doctests
+        run: cargo test --workspace --doc
+        env:
+          RUST_BACKTRACE: 1
+      - name: Check `cargo doc` for lint issues
+        env:
+          RUSTDOCFLAGS: "--deny warnings"
+        run: cargo doc --workspace --no-deps