Very good question. You can see that no scholars here can answer this question.
It really depends on which school you follow.
In the Theravada school, the Surangama Sutra does not exist: the Surangama Sutra exists only in the Mahayana school. Many of those here are answering questions based on the Theravada school, and in a scholarly manner.
The Buddha's Teachings is not about being scholarly or showing off your knowledge! I am not here to write great answers but to clarify.
The Japanese said that Surangama Sutra is not real and written by someone. The someone must be highly wise. The reason for Surangama Sutra being accused of not being genuine is because it contained a lot of actions that we should not do and precepts to follow. The Japanese did a lot of those forbidden actions.
Welcome to the Kali Yuga period or Dharma Ending Age or Apocalypse.
In the Kali Yuga period, the Buddha's Teachings will become an academic exercise like what is happening here. How scholarly with your knowledge.
The Surangama Sutra will be the first sutra to disappear in the Kali Yuga period.
Inside the Surangama Sutra, there is the Surangama Mantra which is now separated from the Sutra as a standalone. This is the daily morning recitation mantra, that all Mahayana Buddhist temples in the world recite (when sky is still dark).
It is the most important part of the Surangama Sutra in contemporary Mahayana Buddhism.
However, the Surangama Sutra is losing its importance in contemporary Mahayana Buddhism. The reason being it is a long sutra to be recited, and it is not easy to understand if it is in Chinese.
The best book on Surangama Sutra is Surangama Sutra translated by the late Charles Luk K'uan Yu (he died in 1978).
The late Master Hsuan Hua and his disciples did some translations. It is available on their web.
The Warning to practitioners section really tells you what will happen when you reach a certain stage. It is a good warning.
In order to recite the the Surangama Sutra, the person must be a full time vegan without eating the 5-6 pungent items -- some Mahayana monks said. I am not sure about being a full time time vegan only you can recite the sutra. Don't try reciting it unless you want to invite demons and devils to fight with you in the first place. Read it first.
Not many can do so, then it is losing its appeal.
So Surangama Sutra and Mantra only exist actively in temples. Externally it is just another book with a few that will recite.
As far as I know there's never been any "school" which based itself on its interpretations, unlike the Mahaparinirvana, hua-yen, lotus, etc.
All schools are the same -- upekkha or equanimity.
Hua Yen-Avatamsaka sutta a great book that I will fall asleep reading.
What is there to interpret about? It is a straightforward book. Use it in your meditation and daily life.
Where can I find out about its historical and contemporary use?
Read the whole book. The Surangama Sutra is about Ananda and Matangi: yes, Matangi. The mantra is about breaking breaking evil spells like Atanatiya.
Contemporary use -- it is not about theory and exorcism. It is all there.Read it.
Usually more suited for monks and upasakas who had been monks before.
If you don't understand, please seek more clarification from me.
The cult endless attacks on Nalanda University put the Surangama Sutra existence only in Chinese after Chinese monks brought it back to China before the 12th century. The destruction of Nalanda University dealt a big blow not only to the Buddha's Teachings but to the Sanskrit Surangama Sutta existence. All important knowledge destroyed and later claimed by the cult.
Many cult students attended the Nalanda University before they informed their blood brothers to destroy all the knowledge that should be left to us.