[libc++][CI] Replace LLDB test targets with libc++ test category (#110856)

We've been increasing the coverage of libc++ LLDB tests in the pre-merge
CI (see https://github.com/llvm/llvm-project/pull/110570). Unfortunately
the tests are spread across different targets. It would be great if we
had a single target that libc++ maintainers could run.

We do this by passing the `libc++` test-category as a parameter to
LLDB's [`dotest` testing
framework](https://lldb.llvm.org/resources/test.html). This will only
run LLDB tests that have been marked as belonging to the `libc++`
category.

libcxx/utils/ci/run-buildbot

@@ -371,14 +371,8 @@ bootstrapping-build)
           -DLLVM_LIT_ARGS="-sv --xunit-xml-output test-results.xml --timeout=1500 --time-tests"
 
     echo "+++ Running the LLDB libc++ data formatter tests"
-    ${NINJA} -vC "${BUILD_DIR}" check-lldb-api-functionalities-data-formatter-data-formatter-stl-libcxx \
-                                check-lldb-api-functionalities-data-formatter-data-formatter-stl-generic \
-                                check-lldb-api-functionalities-data-formatter-data-formatter-stl-libcxx-simulators \
-                                check-lldb-api-commands-expression-import-std-module \
-                                check-lldb-api-lang-cpp-std-function-step-into-callable \
-                                check-lldb-api-lang-cpp-std-function-recognizer \
-                                check-lldb-api-lang-cpp-std-invoke-recognizer
-
+    ${NINJA} -vC "${BUILD_DIR}" lldb-api-test-deps
+    ${BUILD_DIR}/bin/llvm-lit -sv --param dotest-args='--category libc++' "${MONOREPO_ROOT}/lldb/test/API"
 
     echo "--- Running the libc++ and libc++abi tests"
     ${NINJA} -vC "${BUILD_DIR}" check-runtimes