Is there any mechanism to observe or hook into DO lifecycle events?If you mean events like "hibernating" or "shutting down", then it's not supported. The reasoning especially for the shutting down event is that there is nothing to guarantee 100% that the event would be delivered to your application and your handler successfully completing, so your application could become incorrect depending how you use that hook.
Is there a way to detect or handle DO infrastructure level errors (e.g., too many subrequests, overload conditions, subrequest depth limit exceeded), or to access related metadata such as subrequest count, request depth, or parent DO context?It's not clear what "parent DO context" refers to here. But, all DO errors are thrown to the caller Worker and you can inspect their properties to see if they are due to an overload for example. See https://developers.cloudflare.com/durable-objects/best-practices/error-handling/ for details.