How do we put CAST with format with linq to entities in EF core

Define the function(s) you want to call:

public static class SqlFunctions
{
    public static string Format(decimal? value, string format) => value?.ToString(format) ?? string.Empty;
    
    public static void Register(ModelBuilder modelBuilder)
    {
        var method = typeof(SqlFunctions).GetMethod(nameof(Format));
        modelBuilder.HasDbFunction(method).HasTranslation(TranslateFormat);
    }
    
    private static SqlExpression TranslateFormat(IReadOnlyCollection<SqlExpression> args)
    {
        return SqlFunctionExpression.Create("FORMAT", args, typeof(string), null);
    }
}

Register the function(s) in your DbContext:

public class YourContext : DbContext
{
    ...
    protected override void OnModelCreating(ModelBuilder modelBuilder)
    {
        base.OnModelCreating(modelBuilder);
        SqlFunctions.Register(modelBuilder);
        ...
    }
    ...
}

Call the function(s) in your query:

var query = from obj in yourContext.YourTable
            where SqlFunctions.Format(obj.Number, "0.00").Contains("03.1")
            select obj;

NB: You don't need the CAST; FORMAT already returns an nvarchar.

NB 2: If you need the full abilities of the LIKE function, use EF.Functions.Like:

where EF.Functions.Like(SqlFunctions.Format(obj.Number, "0.00"), "%3.[1-5]%")

But for the simple comparison shown in your question, Contains is sufficient.