Batching and Grouped Execution Limits

First, how is batching defined within the group execution context?

Secondly, if we had an incremental ingestion transaction of 3000 items, where we might see grouping of 1x 1000 items, 2 x 500 items, 1000 x 1 items, what are the limits for a function backed action. My understanding is that there would be 1003 groups created that would trigger 1003 automations. For the function-backed action within the automation, can it support the input of an object set of size 1000?

Inputs will be batched according to any batching settings first, then grouped by any grouping keys.

With an object set input (i.e. batched or grouped execution), the object set size limit is generally unbounded (and will support a set of size 1000); however, in the example you give, all 1003 groups would execute in parallel, so it’s possible you may run into rate limiting depending on the effects you choose to execute.