Part of #19303.
Replace ArgsManager::cs_args from RecursiveMutex to Mutex.
The conversion follows the pattern established in prior RecursiveMutex removals (e.g. CAddrMan in #19238, CBlockPolicyEstimator in #22014): extract private lock-held helpers with trailing underscore naming (GetSetting_(), GetArgFlags_(), GetPathArg_()), then replace recursive calls in methods that already hold cs_args with those helpers.