This is actually something I've been a bit confused about for a while. Are runesmiths also trained as full blacksmiths, jewelers, and weavers? Snorri's made all the major weapons and armor himself but at times when he's doing bulk orders he's taking orders from blacksmiths and jewelers. So like do runesmith apprentices get 3x the workload of other apprentices because they have to learn multiple trades?
Snorri makes his own bases for applying runes most of the time, and not just for his most prestigious commissions. He made all of his retainers' gear, for example, if you recall. So Snorri is at least a blacksmith and a metallurgist and a jeweller and a leatherworker and a sculptor and a stonemason in addition to his main gig as a carver of runes, and he's picked up whittling and painting and probably a bunch of other stuff as well as part of his toymaking hobby. He expects his apprentices to achieve competence in at least some of these areas before graduating, too, although probably not all of them at once (see K & N forging axes, Snerra doing sculpting work on the miner, etc). The only instance I can think of where Snorri conspicuously does not do the base work himself is on siege engines; those he leaves to the pros, as far as we've seen.
Of course, Snorri is atypical in a lot of ways and we shouldn't immediately conclude he's representative of runesmiths everywhere. For one thing, his own apprenticeship lasted all of 20 years and, given how much of that time would have gone into teaching him to make functioning runes at all, I don't think it can have been physically possible for Yorri to instruct him in all of these other trades as well. I'm sure there are transferable skills from runesmithing to eg. mundane blacksmithing but Snorri would still have to have picked up most (all?) of his various other abilities on his own. Which is maybe not super surprising, at the end of the day, given that he is 1) deeply, instinctively curious and 2) probably in the top 5 biggest workaholics in the universe. Whenever he's had a moment of respite these last 800 years he's probably thrown himself into learning gemcutting, or glassmaking or whatever, until he became the curmudgeonly old omni-artisan of today.
As for what, besides runecrafting, an apprentice runesmith is generally expected to learn before striking out on their own, who knows? Snorri clearly thinks they should know to do more than just put runes on things but I really couldn't tell you if his views are shared by the majority of masters. I've posted before about how his own journey was probably super tough, and I think it might have coloured his perceptions of how long an apprenticeship ideally ought to take: he was pushed out the door way before he felt himself ready and, when he started teaching himself, went to the opposite extreme and kept his apprentices under his wing for 100+ years. Part of that is because he expects them to learn every standard rune he knows, but I figure he also favours giving a broader education than Yorri gave him (and maybe than the average runesmith gives their pupils).