There's no need to apply distinct() since you're storing the data into the Map and keys are guaranteed to be unique.
You can flatten the entries of the source map, so that only one string (let's call it name) and a single integer (let's call it number) would correspond to a stream element, and then group the data by string.
To implement this problem using streams, we can utilize flatMap() operation to perform one-to-many transformation. And it's a good practice to define a custom type for that purpose as a Java 16 record, or a class (you can also use a Map.Entry, but note that approach of using a custom type is more advantages because it allows writing self-documenting code).
In order to collect the data into a TreeMap you can make use of the three-args version of groupingBy() which allows to specify mapFactory.
record NameNumber(String name, Integer number) {}
Map<Integer, List<String>> dataByProvider = Map.of(
1, List.of("a", "b", "c"),
2, List.of("a", "b", "z"),
3, List.of("z")
);
NavigableMap<String, List<Integer>> numbersByName = dataByProvider.entrySet().stream()
.flatMap(entry -> entry.getValue().stream()
.map(name -> new NameNumber(name, entry.getKey()))
)
.collect(Collectors.groupingBy(
NameNumber::name,
TreeMap::new,
Collectors.mapping(NameNumber::number, Collectors.toList())
));
numbersByName.forEach((name, numbers) -> System.out.println(name + " -> " + numbers));
Output:
a -> [2, 1]
b -> [2, 1]
c -> [1]
z -> [3, 2]
Sidenote: while using TreeMap it's more beneficial to use NavigableMap as an abstract type because it allows to access methods like higherKey(), lowerKey(), firstEntry(), lastEntry(), etc. which are declared in the SortedMap interface.
Mapand populate the result directly in that loop. There's no need to create adistinctStringsList.