The storage_proxy::stop() is not called by main (it is commented out due to #293), so the corresponding message injection is never hit. When the test releases paxos_state_learn_after_mutate, shutdown may already be in progress or even completed by the time we try to trigger the storage_proxy::stop injection, which makes the test flaky.
Fix this by completely removing the storage_proxy::stop injection. The injection is not required for test correctness. Shutdown must wait for the background LWT learn to finish, which is released via the paxos_state_learn_after_mutate injection. The shutdown process blocks on in-flight HTTP requests through seastar::httpd::http_server::stop and its _task_gate, so the HTTP request that releases paxos_state_learn_after_mutate is guaranteed to complete before the node is shut down.
Fixesscylladb/scylladb#28260
backport: 2025.4, the `test_lwt_shutdown` test was introduced in this version
Closesscylladb/scylladb#28315
* https://github.com/scylladb/scylladb:
storage_proxy: drop stop() method
test_lwt_shutdown: fix flakiness by removing storage_proxy::stop injection
a41d7a9240