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

could you explain the usage of 'up' in 'what are you up to'? I know what that phrase means but I don't really get what 'up' means in that phrase

does it have similar meaning as up next, or up for auction?

"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.