Generate Random samples per category

Here is another method to try. I have attached the pbix file as the explaination is too long for a post.
It will look for new users in a week and determine the number of samples to pull for that user based on the week. 
End result...

You can amend it to fit your needs as you see fit. 
It assumes that the number of cases added for a user is greater or equal to the number of samples that would be required. And, you may see duplicate selected cases. You can use the 'refresh preview' button to cycle the requests until you get unique numbers.

It assumes that the week data is coming is as separate queries.

let
    reportWeekStart = 
    Date.WeekOfYear(#date(2025,07,04)),
    combineWeeks = 
    Table.Combine({WeekOne, WeekTwo, WeekThree, WeekFour}),
    add_week_of_year = 
    Table.AddColumn(
        combineWeeks, 
        "WeekOfYear", 
        each Date.WeekOfYear([Date]), 
        Int64.Type
    ),
    group_user_week = 
    Table.Group(
        add_week_of_year, 
        {"User", "WeekOfYear"}, 
        {{"Count", each _[CaseNumber], type list}}
    ),
    add_report_week = 
    Table.AddColumn(
        group_user_week, 
        "ReportWeek", 
        each 1 + ([WeekOfYear] - reportWeekStart), 
        Int64.Type
    ),
    Source = 
    Table.Group(
        add_report_week, 
        {"ReportWeek"}, 
        {{"Count", each _[User], type list}}
    ),
    add_new_user_list = 
    Table.AddColumn(
        Source, 
        "Custom", 
        each 
            try List.Difference([Count], Table.SelectRows(Source, (x)=> x[ReportWeek] = [ReportWeek] -1)[Count]{0}) 
            otherwise {}, 
        type list
    ),
    add_user_sample_count = 
    Table.AddColumn(
        add_new_user_list, 
        "CombinedList", 
        each 
        let
        repeatedList = 
            List.Zip(
                {
                    List.Difference([Count], [Custom]), 
                    List.Numbers(1,List.Count(List.Difference([Count], [Custom])),0)
                }
            ),
        newList = 
            List.Zip(
                {
                    [Custom],
                    List.Numbers([ReportWeek], List.Count([Custom]), 0)
                }
            )
        in 
        List.Combine({repeatedList, newList}),
        type list
    ),
    expand_user_sample_count = 
    Table.ExpandListColumn(
        add_user_sample_count, 
        "CombinedList"
    ),
    extract_values = 
    Table.TransformColumns(
        expand_user_sample_count, 
        {"CombinedList", each Text.Combine(List.Transform(_, Text.From), ","), type text}
    ),
    split_sample_count_to_columns = 
    Table.SplitColumn(
        extract_values, 
        "CombinedList", 
        Splitter.SplitTextByDelimiter(",", QuoteStyle.Csv), 
        {"User", "Samples"}
    ),
    remove_columns = 
    Table.RemoveColumns(
        split_sample_count_to_columns,
        {"Count", "Custom"}
    ),
    add_user_cases = 
    Table.AddColumn(
        remove_columns, 
        "Cases", 
        each 
        let 
            week = [ReportWeek], 
            user = [User] 
        in 
            Table.SelectRows(
                add_report_week, 
                each [ReportWeek] = week and [User] = user)[Count]{0}, 
        type list
    ),
    set_types = Table.TransformColumnTypes(add_user_cases,{{"Samples", Int64.Type}}),
    create_random_list = 
    Table.AddColumn(
        set_types, 
        "RandomPosition", 
        each 
            let 
                samples = [Samples], 
                caseCount = List.Count([Cases])-1 
            in 
                List.Generate(
                    ()=> 0, 
                    each _ < samples, 
                    each _ + 1, 
                    each Number.Round(Number.RandomBetween(0, caseCount), 0)), 
            type list
        ),
    select_random_cases = 
    Table.AddColumn(
        create_random_list, 
        "RandomSelectedCase", 
        each 
        let 
            caseList = [Cases] 
        in 
            List.Transform(
                [RandomPosition], 
                each caseList{_}
            ), 
        type list
    ),
    select_needed_columns = 
    Table.RemoveColumns(
        select_random_cases,
        {"Samples", "Cases", "RandomPosition"}
    ),
    expand_sample_cases = 
    Table.ExpandListColumn(
        select_needed_columns, 
        "RandomSelectedCase"
    )
in
    expand_sample_cases