Background check - lacking contract for company title

Hi, I am currently applying for summer internships in 2022 and have proceeded to the first steps in some recruiting processes. I was formerly employed at a company for 2,5 years. After 1,5 years one of my managers left to run another division and they needed someone to temporarily step up until a new manager could be found. I was given a temporary role which was supposed to last for 2-3 months. They were happy with my performance so this temporary role just got extended time after time. Eventually, I quit in order to study abroad after having worked in the temporary role for about a year.

The problem is that since this was a temporary role, there are no actual contracts confirming my promotion to the temporary role. All I have is an oral agreement with my former manager. I have used the title of my temporary role on my resume. I have a letter of recommendation from my former manager confirming my role. Also, my manager will act as a reference and will without any doubt confirm my role to anyone that might ask. However, if they were to call HR at my former employer and ask regarding my temporary role with title X, they would be clueless. I am now wondering, do European offices of investment banks call the references that I provide for background checks, or do they send a request to HR?

I'm really worried that this will cause me to fail background checks. What would you do in my situation?

Thanks in advance!