feat(tui): builtin UI (TUI) sets client info #30397

Problem:
The default builtin UI client does not declare its client info. This
reduces discoverability and makes it difficult for plugins to identify
the UI.

Solution:
- Call nvim_set_client_info after attaching, as recommended by `:help dev-ui`.
- Also set the "pid" field.
- Also change `ui_active()` to return a count. Not directly relevant to
  this commit, but will be useful later.

test/functional/testnvim.lua

@@ -458,7 +458,7 @@ end
 --- @param argv string[]
 --- @param merge boolean?
 --- @param env string[]?
---- @param keep boolean
+--- @param keep boolean?
 --- @param io_extra uv.uv_pipe_t? used for stdin_fd, see :help ui-option
 --- @return test.Session
 function M.spawn(argv, merge, env, keep, io_extra)