What is the validity of the SQL Server index when using EntityFramework?

This is the first development in the Entity Framework 6, ASP.NET (MVC) project (C#).
DB is the Azure SQL database.
We created a non-clustered index on age because the ID is the primary key and the member table with columns such as name, age takes a long time to search.
If you look at the execution plan below, it will be a key reference to get the name data.

select id, name, age from member where age>=25

To avoid this, it would be better to create a composite index or include option in (age, name).

This raises my question, but in the case of EntityFramework, we obtain it as follows:
I think I got all the columns because I didn't specify a SELECT clause, but does it mean that the index doesn't work?

using(vardb=new SampleContext())
{
    varquery=db.member.Where(m=>m.age>=25);

    foreach (var member in query)
    {
        Console.WriteLine("id={0}, name={1}, age={2}", member.id, member.name, member.age);
    }
}

If I use EntityFramework, will the index become meaningless, and if so, I would like to ask you how to reduce the processing time.
I'm a beginner, so I'm looking forward to working with you.

(Additional)
Attempted to retrieve SQL using the code below.

using(vardb=new SampleContext())
{
    db.Database.Log=sql=>{Console.WriteLine(sql);};

    varquery1 = db.member.Where(e=>e.age==25);

    varquery2=db.member.Where(e=>e.age==25).Select(e=>new{e.id,e.name,e.age});
}

// query1
// SELECT 
//    [Extent1].[id] AS[id],
//    [Extent1].[name]AS[name],
//    [Extent1]. [mail_address] AS[mail_address],
//    [Extent1].[type] AS[type],
//    [Extent 1]. [age] AS [age]
//    FROM [dbo]. [member] AS [Extent1]
//    WHERE [Extent 1]. [age] = @p_linq__0
//
// query2
// SELECT 
//    1 AS [C1]
//    [Extent1].[id] AS [id]
//    [Extent1].[name]AS[name]
//    [Extent 1]. [age] AS [age]
//    FROM [dbo]. [member] AS [Extent1]
//    WHERE [Extent 1]. [age] = @p_linq__0

When I looked at the execution plan in SQL, I found that both were 100% clustered Index Scan with only the primary key (id).
When indexing with the Include option as shown below, query1 was 50% Index Seek, 50% Key Reference, and query2 was 100% Index Seek.
CREATE INDEXIX_member ON member(age) INCLUDE(name)

When I measured the processing time about 100 times, it was about 30 milliseconds on average, but query 2 was slower.
Since most of the existing programs use query1, does that mean that the index is not very effective?

Is it an ant to use the Include option to specify all other columns?

I'm sorry that it's my first time using this.Thank you for your continued support.