For each category find first negative value and then keep at zero

You can calculate the first negative year by filtering for negative values and grouping on the first three columns and taking the minimum over the Year column. Merge this minimal year calculation back into your original table and compute [New value] using a comparison between Year and FirstNegativeYear.

Sample query you can paste into the Advanced Editor in your query editor:

let
    Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("bY7BDcAgCEV34awJoCTtse0Yxv3XEJHUJuVAvuH5gNaAIMGlNZORDg1B6OlHTouAaDNBphDRllift1bZkkRgKj5sdh77916Ql1N9Td2kYEDWbX6B+CL+jCMOkFlVpT4A", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type nullable text) meta [Serialized.Text = true]) in type table [Group = _t, Category = _t, Country = _t, Year = _t, Value = _t]),
    #"Changed Type" = Table.TransformColumnTypes(Source,{{"Group", Int64.Type}, {"Category", type text}, {"Country", Int64.Type}, {"Year", Int64.Type}, {"Value", Int64.Type}}),
    #"Filtered Rows" = Table.SelectRows(#"Changed Type", each ([Value] < 0)),
    #"Grouped Rows" = Table.Group(#"Filtered Rows", {"Group", "Category", "Country"}, {{"FirstYearNegative", each List.Min([Year]), type nullable number}}),
    #"Merged Queries" = Table.NestedJoin(#"Changed Type", {"Group", "Category", "Country"}, #"Grouped Rows", {"Group", "Category", "Country"}, "Grouped Rows", JoinKind.LeftOuter),
    #"Expanded Grouped Rows" = Table.ExpandTableColumn(#"Merged Queries", "Grouped Rows", {"FirstYearNegative"}, {"FirstYearNegative"}),
    #"Added Custom" = Table.AddColumn(#"Expanded Grouped Rows", "NewValue", each if [FirstYearNegative] <> null and [Year] >= [FirstYearNegative] then 0 else [Value], Int64.Type)
in
    #"Added Custom"