Just like we did previously in e.g. #78672 we can make the string in LIFECYCLE_NAME_SETTING a field in Indexmetadata so we don't have to look it up for every index on every cluster state update in the lifecycle service.

This setting alone currently takes almost 1% of the overall master runtime (and more than that in terms of wall-time I would assume) when creating the initial indices set during many-shards benchmarking:

relates #77466