Would use of decaffeinated tea promote health in my case, and generally, or is such caffeine exposure actually beneficial to health in some way?

Caffeine can be beneficial, that is why it exists in nature, it has multiple roles in multiple types of organisms and it will be something that is beneficial for humans, and it is only in those where a chemical imbalance happens because of their particular chemistry where too much of a good thing will cause inner disquiet. If that is not the case for an individual, caffeine can be ingested daily with no long-term consequences to health.