So I'm curious what role does a Padawan play in their Master's life? Or is supposed to by Temple expectations? In The Clone Wars it is stated a few times that Ahsoka’s job is to "watch Anakin’s back" and "keep an eye on him." Which in context seems to be about ensuring his safety and keeping him reminded of the Code. Now, my Wife is reading the Jedi Quest books rn, and those are so far very centered on Anakin learning by doing/watching Obi-Wan and other Knights. But like, would a Padawan ever have to fetch their Master's caf, or iron their robes for them? It isn't uncommon for real world Apprentices to have to fulfill mundane tasks for their Master's, is there any indication in Canon or Legends that the Padawan may play a bit of an assistant role at times?
I don't know if they ironed robes or fetched caf, but I would absolutely expect padawans to help their masters with mundane aspects of the profession. When I was training as an aircraft mechanic, I absorbed a lot of knowledge while holding the flashlight for my instructor and handing him tools. Learning to fly, there was a lot I learned by watching the instructor pilot at the controls while I monitored the fuel consumption, filled out the maintenance and flight logs, calculated cargo loads, etc. It wouldn't surprise me a bit if there was also some aspect of "I had to do these things for my master so now my padawan needs to do them for me." That's just life.
Being an apprentice, I think, is meant to be a lot different from the training one might receive as an Initiate. Initiate classes would have been standardized to cover the basics. As a result, going into being a Padawan every new apprentice would probably have the same skill sets and the same common knowledge. But one on one apprenticeships seemed to be much more tailored to the individual Master's experiences. And Masters themselves seemed to have pretty wide latitude in how they taught their apprentices. For instance, in the novel Rise of the Red Blade, Iskat the apprentice is basically treated like an unpaid intern/research assistant by her Master. In the game Jedi Fallen Order Jaro Tapal is more of a drill instructor from what we can see of him, and has his apprentice Cal focusing more on physical training. Despite the differences we see in how Padawans are trained, one common viewpoint seems to persist; you learn on the job. Being a Padawan seems to be a sort of sink or swim type of learning environment. Your time in the Temple, nice and safe, is over and done with for the most part. You have to go out, get your hands dirty, and gain some practical experience. That practical experience takes on several forms; be it fighting criminals, resolving disputes, or simply doing research in the field. The idea is to watch and learn by example. Gain an understanding of the varied environments and people's you might have to work with as a full Jedi. I base this partially on the notion raised in the novel Into the Dark, where Master Jora Malli acts as though her apprentice Reath Silas's unwillingness to work on the frontier will stunt his development. You could theoretically stay in the temple and pass your trials, but you'd be doing a disservice to yourself. And, I assume, part of that training would be self reliance. How to mend your clothes in the field. How to prepare your own food. How to administer first aid. Running the occasional errand might not be universal as a teaching method, but it might be a way for a Master to start small in teaching an apprentice how to handle small issues before working them up to bigger problem solving.
Given humility is a key cornerstone of a Jedi's life I doubt Masters are expected to give their Padawan's mindless busy work. We've never seen a Master ask their Padawan to do something that wasn't an immediate and direct learning experience as far as I am aware. I'm pretty sure Master and Apprentice makes mention of Padawan's having homework so there still seems to be an academic side to the Jedi training.
But it was also a Master's job to pass on those lessons about humility and the importance of completing even the most mundane tasks. So while I would not expect a master to set a padawan on a chore just to keep them out of their hair...I could see them giving them assignments a padawan may see as undignified or insulting to their perception of themselves. A lesson for the padawan to check themselves. ---------- As to a padawan's role in general...I think Ahsoka is actually a bad model on which to base our expectations of padawans in general, just as Anakin is a bad model for the typical master. I think Ahsoka was specifically chosen by the council to mentor with Anakin because A) she was unusually capable already and B) was willful enough to not take all Anakin's boasts and stumbles as proper or ideal to follow. In many ways, Anakin and Ahsoka turn an instructor/student relationship into more a partnership fairly quicky, even if a senior/junior partner type. This is quite different from the relationship we see with Obi and Qui Gon, which was much more teacher/student, much more reverential, and much more structured, which is ironic given Qui Gon's less than obedient track-record with the order. Now could the war be the cause for the difference? Probably a substantial part. But I would argue if not for the war, Anakin would not have a Padawan at all at that stage. He may not get a Padawan until he became a Jedi Master if it was peacetime. He may never get a Padawan at all. I think we the audience were to infer from the get-go that Anakin/Ahsoka was something of an odd-couple. They were not standard practice for the Jedi order. So looking for expectations there is not a good place to start.
The Clone Wars certainly changed the role of a padawan pretty significantly. Ahsoka being there to watch Anakin's back is pretty much Anakin's take on it in war. I can't see Obi-Wan saying that to Anakin in years of peace or on assignments that weren't potentially martial in nature. No doubt Padawans had to do som very mundane stuff that they didn't particularly enjoy. As noted, the humility piece is pretty key and wouldn't be out of place in the kind of spiritual order relationship that is common in real world traditions. Being a Jedi can be a mix of martial arts master, diplomat and spirituality. If the master has their Padawan shine their boots or wash their robes, it's just part of it. A lot of what the Padawan is going to be doing is observation. Keeping quiet a lot of the time. Partnered training drills, guided meditation, watching and listening when in diplomatic or consultative situations, and watching the master's back in a fight or a potentially violent situation. I learned a lot by observation when I was at an early stage of my apprenticeship as a wallpaper hanger, I also had to do busy work tasks just to give me something to do until I had a more useful skill set. I was given tiered tasks that led me to cultivating the skills of a wallpaper hanger. I also spent a long time observing how to interact with clients. Sometimes I just had to make coffee runs. Sufi teachers are supposed to have such a relationship with their students that they perceive what character traits need work, where they need to be humbled and what tasks might be a challenge for their egos, and assign them accordingly to break their students of their egos. So, I could see a Jedi Master similarly doing that with a Padawan.