Maybe a couple of useful things for you here..
examine can struggle to find integers down to the whitespace analyser (default if memory serves)
a work around is range query.. Examine, cannot search with parentID, why? - Umbraco community forum
Also if you are searching for ids in the path, if that’s all you want then I think the improvements to the content/publishedcahe/media repositories there have been published tests that show the examine is actually slower than a linq query… though obviously your use case will dictate.
There is also a package Search Extensions | Umbraco Marketplace that extends in all the ways I think you are asking. 