TL;DR: My current position does not afford me the opportunity to gain experience in some tasks that are viewed as standard junior level tasks for my industry. How does this affect my chances of getting a job with the same title/responsibilities at a different company?

Introduction

For the past 2.5 years, I have worked as a contractor in an junior/early career capacity at a small company that provides onsite technical support/assistance to a federal agency. Let's call my position's title: Worker. Let's also say that I earned my degree in Working. I have done fairly well in my capacity as a Worker and the government PM (who I essentially report to) at this federal agency holds me in high regard with respect to my abilities, competency, and work ethic (said PM is vocal of their satisfaction and has encouraged me to apply to vacant federal positions within the agency).

With all this being said, my job responsibilities as a Worker in some respects are quite different when compared to say someone who is a Worker with the same years of experience as me but at a different company. A general example of this might be: A Worker in my industry is expected to do task X which is
generally considered to be the real first step in becoming a more senior Worker in industry, while I as a Worker with the same years of experience am expected to observe/oversee the execution of task X without ever having performed this task professionally. As my education has given me the training and skill-sets to understand the "ins and outs" of task X and how it should be performed/excuted, to me it doesn't seem inappropriate for me to observe/oversee task X. That being said, I have never performed task X professionally nor will I ever been give the opportunity in my current position.

It should be noted that my time in this position has also given me a lot of responsibilities that only mid to senior level people are tasked with. The flip-side to this is that in being given nontraditional roles and responsibility as a junior staff, I have not been given the more traditional junior duties that most people with my time and experience are given.

Problem

It is likely that my contract will not be renewed in the coming year and as such I am looking to secure new employment as a Worker but at a different company. I am looking to stay in the same industry as well.

I have applied to multiple junior/early career Worker openings that are commensurate with my experience,education, and training at various other companies but as of yet, I have not secure new employment. I have interviewed a few times but no offers.

Question

What is the likelihood that my nontraditional career beginnings will have a negative affect on my chances of getting a job as a early career Worker at a different company in the same industry?