Cleanup PathTrie

[dakrone]

From #25459:

We should further refactor PathTrie so that the params of RestRequest are not modified for each TrieMatchingMethod, and switch PathTrie over to using an FST from Lucene, rather than our own trie implementation.

Additionally, PathTrie should use the builder pattern so we create an immutable object rather than modifying the existing one.

[antbac]

I represent a group of people who would like to contribute to this issue, but seeing how I can't assign myself I'll just write this comment to notify you.

[nik9000]

I represent a group of people who would like to contribute to this issue, but seeing how I can't assign myself I'll just write this comment to notify you.

@antbac, I know its been almost a month, but, sure! If you are interested then please have a look at it. I suspect that this is a fiddly issue to solve so it'd be nice if you posted some kind of work in progress PR before going super deep.

[antbac]

Sorry for the very late reply, but I am affraid our group has dispanded. We were unable to produce any satisfactory results so I won't be pushing a pull request.

[thecoop]

I'm going to fold this into #107425 to consider as part of that work