Validate index settings after applying templates

[jasontedor]

Today we validate index settings before applying templates. While this does not cause a problem in general (since if there is a problem we will end up failing on index creation anyway), there is one case where it does cause a problem: checking whether or not the index creation will bring the cluster over the shard limit per node. This is because the only time this limit is checked is when index settings are validated. If we are doing this before applying templates, we would not have the correct number of shards used to check the limit. This commit addresses this by first applying templtes before validating index settings. This addresses the case of checking the shard limit per node, but also will help prevent additional bugs like this in the future. Note that we can not add in any private settings until after the validation is done (otherwise they will fail validation).

Closes #44567
Relates #34021

[elasticmachine]

Pinging @elastic/es-core-features

[jasontedor]

This approach is flawed because of resizing indices, where we copy settings including private settings, and this is what we would want to validate in an approach like this. Since settings validation is fairly simplistic at this point, I am going to take the simpler approach of merely moving the check shard limit out of validation and after templates have been applied. I will close this PR and open another.

[jasontedor]

Superseded by #44619