I see two possible approaches for the interview: either oversell your skills and remain in the running for the offer, or undersell and get passed over. In my experience, one of the main turnoffs for the interview panel is when a candidate highlights their own shortcomings, especially if such criticism is not directly requested (e.g. "what are your main weaknesses?").
We live in times of grade inflation, degree inflation (masters is the new bachelors?), resume inflation, and job title inflation. Whether we like it or not, the reality is when we step into the inteview room, we have already somewhat oversold ourselves. So has every other candidate...it is not a matter of if, but only a matter of degree. Considering the alternative, the issue is not whether you are perceived as capable of more challenging work...
It sounds like you are trying to walk the middle ground of neither over, nor under-selling yourself, but inevitably end up overshooting and getting more that you bargained for. Or so it seems -- to you.
Assuming your interview responses are an adequate reflection of actual ability, this suggests that the actual problem here is not the "problem" as you state it (i.e. "my self presentation skills"). The problem is that "I have no clue if I am up to those challenges" -- aka "cold feet."
One cause of anxiety about being able to meet expectations is insecurity which has to do with a personal tendency for perfectionism and fear of being perceived as someone less XYZ (competent, able, smart, experienced, fill in the blank) than you want to appear. This causes an anticipation of some type of conflict resulting from the unmet expectations, and/or "cognitive dissonance" from a tension between your self-perception and others' perception of you.
The responses to conflicts are on a spectrum with two ends: fight or flight. Digging in and confronting the challege, or avoiding it by escaping the situation. Talking about "sitting here and I have no clue if I am up to those challenges" suggests to me that you are leaning toward the latter. One consequence may be "premptive retreat," i.e. turning down an offer to avoid the anticipated future conflict.
Here it helps to keep in mind that someone else with an identical (or even inferior!) skill set to yours, who is more open to confrontations, will stay the course and give the job their best shot. Such individuals often end up persisting in a position far longer. Part of their strategy is counting on others' aversion to conflict, and using that to implicitly reinforce their position ("you think I suck? but you don't want to tell this to me? oh well too bad for you!"). They may not even be doing this consciously, but the result is the same: they get to stay in the role, while someone who cares more deeply about what others think of them take preemptive action and retreat from the role.
I encourage you to reflect on your past experience, background, and personality traits, to see if you can understand the root of your anxiety about your ability or how others might judge it/you. One key strategy here is learning to separate your professional identity from your real "self". We all put on a certain face on the job, act a certain role - nobody is hired to just "be themselves"; we are hired to do a certain job the best way we know how. That's the expectation.
If you honestly consider yourself a responsible, reasonably capable, disciplined, and conscientious individual who strives to self-improve, learn, and work effectively with others, then what others think of you at work rarely becomes a real and major problem for your success or career, unless you let it be one. Good luck!