Staying in Uk and switching from tier 4 to tier 2 visa

Greetings,

I read before on this forum that if I studied in UK on a tier 4 visa, and wanted to stay in Uk after the end of my master degree, I have to provide an unconditional consent from my previous official financial sponsor.
I know that applies only if:
1- this sponsor was full, covering both tuition fees and living costs. AND
2- provided by the government or an international scholarship agency AND
3- it was within the last 12 months.

This means if my sponsor was an international company, a university or UK independent school, I don’t have to provide the consent if I want to stay or re-enter UK.

In my case, my master degree was fully sponsored by the Islamic Development Bank Scholarship (a financial institution which is located mainly in my country and has many branches around the world, and it provides fully sponsored scholarship for students to continue their studies). I am actually very confused wether this is considered an international scholarship agency or an international company, and wether I need to provide their consent if I want to stay and work in UK.

Please note that it was mentioned in the scholarship contract that I need to return to my home country. So, will this affect my condition?

I really appreciate your help.
Thank you