[REQUEST] Muon Optimizer - Different LR for Different Groups

Is your feature request related to a problem? Please describe.
When using Muon optimizer, now the method is to setup that in config. Params will be grouped into muon & adam automatically per #7555. However, there's a single LR that passed into both groups - this is not the standard pattern. We should have different LR for the muon group and the adam group (usually, muon should have larger LR). I wonder if there's a way to enable this behavior easier from my side. If not, then we probably need to add a support for different LR.

Describe the solution you'd like
Easiest way to achieve this is probably to have "muon_lr" and "adam_lr" instead of a single "lr" key. Then in different groups, fetch accordingly.

No file or test is named. Start by tracing the Muon optimizer configuration and the automatic Muon/Adam parameter grouping described here and in #7555. Determine where the shared lr is applied, then verify that separate muon_lr and adam_lr values are accepted and used by their respective groups.