Quite a few people, including riverwalk and shizam make the point that one can overthink this. Why do you need to "carve out a role" at all? Wait to be asked, make it clear you are there to support if asked, be glad for the new parents, but don't worry now about what your "role" wolll be.
This is their baby, not yours and (sorry to say this) but you must vet down the ladder of importance in the family!
I think over eagerness to play an active part in a grandchild's upbringing is a recipe for disaster and we have seen examples on GN of grandparents overstepping the mark, muscling in, interfering, antagonising DIL or SIL, giving unwanted advice and generally not being willing to let go of their adult children or let them assume their role as grown up parents themselves.
I am not suggesting you would fall into any of these traps or that your motives are anything but the best, but it's not about you, or us, it is about the young family.
Do NOT let envy raise its ugly head. You don't live on the doorstep and you say you are still working, so time will be restricted anyway. If you have a good relationship with your DS and DIL the rest will follow naturally. Invite them from the day orbthe weekend, visit, but stay in a hotel if you are staying overnight, give plenty of notice instead of arriving unannounced somtounwon't have false expectations and basically be have to them as a family as you do to them as a couple. Sorry to have gone on so!!