I feel like once I get in the engineering group, things will be fine, but the delays with the recruiter are making me have second thoughts about what otherwise was a very exciting prospect.
Is slow communication indicative of bad communication throughout the company, or just a fluke? Should I be worried?
If it comes through as expected, great, you can evaluate your options at that point. Until then, you should hope for the best, but plan for the worst, these things can and do get cut off at any time, nothing is final until your first day.
This is indicative of bureaucracy, not bad communication. This advice applies to any kind of business transaction / negotiation like buying a house, car, whatever, talk is good, but it doesn't mean anything and can't be relied upon until its in writing and money changes hands.
Even if the internal recruiter is completely incompetent, the odds of you ever having a future interaction with them are near zero.
It is greatly to your benefit to remain calm, cool, patient, and polite. You never know if the recruiter has to go to bat for you internally. If they don’t like you, they won’t do it.
Good luck!
Edit: I wouldn’t worry. Engineering depts are usually well insulated from whatever nonsense is happening in the HR dept