Guidance needed on using local PBI to extract data from SQL Server on a third-party's VM domain

[D_PBI]

Hi,
I'm having trouble connecting PBI Desktop, on my local machine, to SQL Server installed on an external party's Virtual Machine (VM). I would like to explain the steps taken thus far and to seek guidance on what's going wrong. Bear in mind, I'm not ofay with domain/networks enough to understand what, in that world, could be restricting my access.

Our third-party are using a Virtual Machine in their domain. On this VM they have installed On-Premises SQL Server.
Our third-party have installed an On-Premises Standard Mode Gateway on this VM.
Our third-party have granted me read access on the database.

As our third-party, with the help pf our I.T. department, installed and configured the Gateway, I'm not sure how the connection/recognising works between them installing the Gateway on their VM and it being recognised in our Power BI Service. However, the Gateway is seen from within my own account's PBI Service. My account is a 'Connection Creator' on it. I have successfully managed to create a Data Source on the Gateway (see below). In creating this Data Source you check the connection by default. Connection properties are further below.

At this point, I expecting all is created/configured as needed.
Now, I want to connect PBI Desktop to the source and extract data, from my local PC at my home address. I therefore create the PBI connection as follows:

When creating the Data Source against/on the Gateway (screenshot 2), I have to include the third-party's domain before my username. As I had to do that there, I have also done the same in the above screenshot. The screenshot above shows the connection attempt failed. Even without the domain included it still fails. By the way, the password is what was provided to me and the one used when successfully creating the Data Source on the Gateway.
I understand the Windows credentials route is the correct route to take.
When I try connecting with the Database credentials routes (see below), also including the domain included and without, I get a network error (see further below).

Please can someone advise why I am unable to connect PBI Desktop, on my local PC, to the SQL Server hosted on the third-party's VM?
Thanks.

[lbendlin]

Our third-party are using a Virtual Machine in their domain. On this VM they have installed On-Premises SQL Server.
Our third-party have installed an On-Premises Standard Mode Gateway on this VM.

That's a VBI  (Very Bad Idea). They will fight for the CPU and RAM on that VM.

I think your third party may misunderstand the way gateways work.  Gateways are brokers between an on-premise data source and the Power BI Azure cloud.  They play no role whatsoever in allowing you and your Power BI Desktop access to the on-premise data source. It is expected that you and your Power BI Desktop are located on-premise and have clear sight of both the on-premise data source and the Azure cloud.

In its essence a Power BI Gateway is a headless Power BI Desktop.