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/client/session.lua

@@ -96,8 +96,7 @@ end
 
 --- @param method string
 --- @param ... any
---- @return boolean
---- @return table
+--- @return boolean, table
 function Session:request(method, ...)
   local args = { ... }
   local err, result