How can I create a filter to filer 2 tables with no connection

For this use-case you need to unpivot your data, since your tables do not have the category designation as rows in a column. Your Table 1 must look like this:

And your Table 2 must look like this:

You can paste this code into a blank query to see how to do this simple transformation on your minimal data:

let
    Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("i45WMlbSUTIH4uDUghKlWJ1oJQsgxxKI/ZMhfEOQCkNDIOGXX6YUGwsA", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type nullable text) meta [Serialized.Text = true]) in type table [category1LevelCount = _t, category2LevelCount = _t, month = _t]),
    #"Changed Type" = Table.TransformColumnTypes(Source,{{"category1LevelCount", Int64.Type}, {"category2LevelCount", Int64.Type}, {"month", type text}}),
    #"Unpivoted Other Columns" = Table.UnpivotOtherColumns(#"Changed Type", {"month"}, "Attribute", "Value"),
    #"Added Custom" = Table.AddColumn(#"Unpivoted Other Columns", "Category", each if Text.StartsWith([Attribute], "category1") then "Category 1" else "Category 2")
in
    #"Added Custom"

After loading these tables, you need to create a simple table that contains the Category selection. You can do this in many ways, but the simplest is probably to click "Enter data" in the Home -> Data tab, and create a 1-column table like this:

We will use this small table to push the Category filter to your two fact tables. When the tables are in the data model, connect them using relationships. In the Model view, it should look like this:

The additional small table will act as a filter on both Table 1 and Table 2 simultaneously, achieving the effect you asked for.

When you get to this point, you can create charts based on the month, Attribute and Value columns from Table 1 to create your first chart. The settings for a clustered bar chart are shown below, this will create one bar per month, with height according to the value column, and colors/attribute in legend according to the Attribute column:

From Table 2 to create your second chart. Use your Categories[Category] column as a slicer, and set the slicer to single-select if you want to force a single-category selection: