Specific to the PR, what you call "compilation" is actually 3 (ok, really 4) steps. I wonder if it would be nice/better to
I wonder if it might be better to collect stats for the specific phases.

Note that this has the same limitation that is already part of Query-related statistics overall - the query string used to create the Query and its plan is not always the same one used to key the statistics. Query statistics are collected/exposed by "concrete" query, but a given query-string might spawn multiple concrete queries in some cases:

1. polymorphic queries ("from java.lang.Object")
2. multi-valued parameters
3. enabled filters
4. EntityGraph