I don’t know if this is helpful; I hope it is a little helpful.
I don’t usually hear “indirect boss”, or “direct boss”. It may sound more natural to say my “immediate boss”, but I can’t say I’ve heard that before. 🙄❓❓❓
At my husband’s work, his immediate superior is the “manager”, the one above him is the “supervisor” and the overseer of the whole department is the “director”.
I think a lot of places are like that, each position has a specific title, but they may vary slightly depending on the company.
In my husband’s case, if he wants to express the idea of his ‘direct boss’, he will say, for example, “I talked to the manager” or “I talked to my manager”... “The supervisor” or “my supervisor said”... “I talked to the director”...
I hope that helps.