can anyone explain why there is 'up' in 'what are you up to?

In my experience with this idiom, when someone is suspicious of another's current or future intentions the suspected one would be described as being "up to no good". I think it implies that there is a moral scale of goodness, with higher up on the scale being better. If you are "up to" the bottom of this scale, then you are "up to no good"! Which is to say you are not at all up, but at the bottom of this scale.

Another take on "being up to" something is when a friend asks another friend with which they desire to reacquaint, or just find out what they are involved with as of late. They will often say, "Hey, James! What are you up to, lately?" or "James! What's up?" or "Whatcha been up to?". This form of "up to" in conversation seems to be like asking "What is uppermost in your mind, thoughts or activities as of late?". It serves well as a conversational "ice-breaker". An ice-breaker being a way to break through a conversational barrier between strangers or friends to get a rapport moving to make good dialogue.

One of the funniest forms of inquiring what someone is up to was the theme of the "WAZZUP" beer commercial: Check it out on YouTube : https://www.youtube.com/watch?v=tauYnVE6ykU

OH! Also, when salespeople are taking turns to wait on customers, when it is their turn "up" can be used as a noun. As in, "Hey, John. That lady just walked in to the showroom looking a 3-series. I'm working another deal right now, so I guess this is your up."

It is also used in sports, especially baseball, where the team at bat has batters ready to go. The next batter from the waiting area stands up, maybe comes up out of a dugout waiting area, walks up to a warm-up area and is said to be "next up to bat" while the athlete currently at the home plate and is said to be "up to bat" or "up at bat".

Possible origin since the usage has been covered. Using a verb to go "up" is most likely counting. If you come across someone counting you are asking what number they have counted up to. OK, up to which number they have counted. So "what are you up to" indicates that "you" are doing something and the inquisitor is asking what.

"It's idiomatic; you just have to learn it that way" seems to be the canonical answer to these types of questions - but I think that only serves to increase the barrier between native and non-native English-speakers.

These location-themed idioms have a pattern, and they reflect the way I consider the ideas presented with them. They're very visual.

So let's look at 'down to business', as was brought up in a comment. 'Up' and 'down' are relative terms - relative, specifically, to gravity. In the universe of ideas, the gravity of an idea flows toward the core of the primary object. In a meeting, you might have a number of peripheral social layers - greetings, pleasantries, small talk, obscuring the core objective: the 'business'. So, getting down to business means to cut through the peripheral matters and to the core matter at hand. Failing to get 'down to business' would mean resting on the upper layers of the shell, making no effort to penetrate deeper.

To the actual phrase in question, 'what [activity] are you up to?', we have the opposite direction of motion. The concepts in play are the activity and 'you'. Your movement is 'up', away from the gravity of something and moving toward an activity. What is that something? It's your natural state. You're investing energy, against your inertia (the metaphorical gravity of your natural state), to continue some activity. That activity is what you are 'up to'. When the answer is 'nothing', the implication is that the speaker is at rest, and therefore is not 'up'.

Continuing with these common idioms, you could have someone 'putting up a front' versus 'not letting anyone in'. The first implies action - raising a barrier to conceal your natural state. The second implies inaction - exposing only what is naturally visible.

Back to 'up', in addition to being up 'to' some activity, you can also be up 'for' it. In that case, the image is more similar to the energy states of electrons, for example. You still have your rest state at the base, and then you have various potential activities orbiting at varying distances from rest - indicating how far, metaphorically, they are from rest (the level of burden, the amount of stress, the required energy/time/money, or whatever the subject uses to qualify activities). While entirely abstract, the speaker that is up 'for' a certain activity is also necessarily up for all activities that they perceive to be closer to 'rest'. Someone who's feeling 'down' is typically not 'up' for much.

Conversely, you can also be 'down' for some activity. In this case, the activity has gravity, and the speaker has to decide whether to submit to it or not. The important difference is that, because the activity has been given gravity, it's typically less flexible. Someone who's up for drinks might not be down for 'drinks at Bar A on Friday at 7'. Being up for drinks allows you flexibility, while being down for the plan implies submission to that plan.

I hope this helps to clarify the way that some (at least one) native English speakers visualize this type of language - even if they don't realize it. Failing to explain this visual aspect of the English language is, I think, a tragic failure. It's the difference between a logical, beautiful language that eloquently expresses abstract thought and a cumbersome, illogical language full of nonsensical idioms.

Up is used in many idioms to mean some variation on "currently the subject or focus," possibly by way of "upon" (in [...] complete or approximate contact with) which is an alternate meaning of many of up's ancestors, etymologically, and many of its counterparts in other languages.

The phrases you mention all seem to have this meaning.

"Up" does have other meanings in other phrases (the leading edge of a (vertical) spectrum, agitated/excited, and others) but those are for another time, I guess.

edit: "Up for auction" might mean "the subject of an auction" or it might be a more specialized usage connected with the auctioneer being elevated above the audience and the items being literally or figuratively brought up to podium to be sold. That's one research bridge too far for me today.

This phrase originated from the phrase, to be "up and about." Meaning you are standing up and moving around. The phrase then changed over time to be used in multiple different fashions such as the one in question. So to say, "what are you up to?" Is to ask what activity has you up and about.