Connect all points with a line to the n nearest points with the same attribute value, where n is the number of points you want to aggregate to a group. You can use different values for n for different attribute values (like based on your example n=6 for value=12).

Then create the convex hull of these lines, dissolve the result and convertt multipart to single part geometries. To do this, proceed as follows:

1. Use Geometry by expression with this expression:

    convex_hull( 
        with_variable (
            'no',
            case
            when value = 12 then 8
            when value = 8 then 6
            when value = 2 then 4
            end,
            collect_geometries (
                array_foreach (
                    with_variable(
                        'val',
                        value,
                        eval ('
                            overlay_nearest (
                                ''pt'',
                                $geometry,
                                filter:=value='  || @val  || ',
                                limit:=@no-1
                            )'
                        )
                    ),
                    make_line (
                        $geometry, 
                        @element
                    )
                )
            )
        )
    )
   

2. Dissolve result

3. Multipart to Singleparts

1. Use Geometry by expression with this expression:

    convex_hull( 
        with_variable (
            'no',
            case
            when value = 12 then 8  -- define here how many points you want to cluster together for each value
            when value = 8 then 6
            when value = 2 then 4
            end,
            collect_geometries (
                array_foreach (
                    with_variable(
                        'val',
                        value,
                        eval ('
                            overlay_nearest (
                                ''points'',  -- adapt the name of your points layer
                                $geometry,
                                filter:=value='  || @val  || ',
                                limit:=@no-1
                            )'
                        )
                    ),
                    make_line (
                        $geometry, 
                        @element
                    )
                )
            )
        )
    )
   

2. Apply Menu Vector > Geoprocessing tools > Dissolve to the result

3. Apply Menu Vector > Geometry tools > Multipart to Singleparts to the output.

Result: Points with value 2 are grouped to groups of 4 , value 8 to groups of 6, value 12 to groups of 8:

Result after step 1 with geometry generator: