There's no real reason to move goods outside of trading (nor send your trader there, but as already stated...).
Well, there is, if you want to lump things there in preparation, because it's effectively a Quantum Stockpile for whatever is taken there during a caravan, left there
by a caravan and remains once it left.
But as you generally want the Depot exposed to the world (at least when the wagons are due, or else they don't come with their majority load of goods) I always try to have a "Tradeable Goods" set of regular stockpiles within easy reach of the Depot (but behind the locked doors/extra-sticky defences of the fortress if I'm possibly getting anything from Vile Forces to kea wandering through).
When I get to know the Liason offers (seeds at 200%? - I can spare some of them; gauntlets at 150%, I'll bash some up...) I set some of the stockpiles to the relevent things I'd like to offer. Generally laid out in 1x11-tile strips (in 11x11 rooms, the way I plan these things) each dedicated to one narrow type of good, initially just one bin, if applicable, and if it visually fills up (from natural or forced movement) then I happily adjust accordingly.
The same with figurines, rings, earrings, amulets, bracelets, crowns, and scepters (regardless of specific demand) and Large Gems. If there's no demand this season, there may be in a future one, and rock-crafts handily eat up any surplus of a boring-stone-type (if I have wooden things, probably elf-bought while offloading surpluses, they get their own piles, just to avoid accidentally insulting the elves themselves in a future mixed-goods swap).
When the traders are announced, the tradeables are handily near to the Depot when selecting them to be moved there. Saves time as mandorfpower diverts en mass to haul everything there, and with the selection of goods (with or without other filtering, any item or bin within single-figures-or-so is probably what I want there, I barely have to check the bin contents). I haul bins as much as possible, though never export them, nor bags if I can help it, though will import bins-of-stuff sometimes more for the bin. Bags too. And barrels, except for the ones of blood. But individual items don't cost much more time if nearby like this.
I should have a good stock enDepoted by the time the incoming goods are unpacked. If I have some high-importance items still stuck many Z away, and maybe a way bit off in X and Y too, in my magma-workshop area that never got them into the pre-trade prep area, I can speed up those by exploiting Dump mechanics to make them a priority/sole job for some selected free bodies to undertake, into a special Refuse zone put close to this other action.
As I've traded, if I've time while waiting for some excellent-quality rings (made since the initial arrival), or somesuch, and have other hands with nothing much important to do, I might check the traded-for goods in-depot and make the trade-out stockpiles, now empty, their perfect recipient (and/or that Refuse staging spot, for things I won't have trouble with spoilage). Clear the stuff out, plus de-Mark For Trade all now-empty bins and maybe mark for Dumping to shuffle them out of the place too. Makes it easier to see what's left as I eke out as much bartering as I feel I need to.
I try to leave nothing still Marked For Trade by the time they pack up, one way or another, and then I've got a little bit of shuffling of trinkets bought from these traders (like items only bought because they fulfill the next Dwarf caravan's idea of being wanted) into the nearby stockpiles, or ultimately further into where I'll find them useful (foods to a central foodstore, bars to near the forges, etc). But, especially if I'm Turtling for the winter, or likely to for any other reason, the Depot is emptied of remaining/remaindered items as much as possible, plenty of time to prep for the next visits...
I imagine it'd be very in-context to have things already there, awaiting the arrival of anyone with exchange on their mind. I envision a lone figure, sat back against a wall, dozing with hat down over their eyes, perhaps a cloak or poncho keeping the sun/snow off them - then the Adventurer arrives with a backpack of loot and/or a stuffed purse that jangles, just a little bit, with a nice dull-metallic sound. The prone figure, always with one eye and/or ear open, leaps up and tugs on a rope, the raised counter-top now falling outwards to reveal the delights hidden just beyond, a stick is pushed and an awning-frame swings forward to afford suitable shelter or merely reveal the painted cloth with the supposed name of the proprieter and the words for 'emporium', or maybe 'bazaar,' in various local and exotic writing systems, some lighter items hung down from the forward bar with twine, to save on horrizontal space. A banner flaps down from a crevice under the mud-brick eaves that proclaims "Deal Of The Day" for something or other (faded so much, it surely has said that for a decade), "Best Prices" (without clarifying for whom they are best) and possibly "Last Shop This Side Of The Desert" or similar, even if it's actually the
first shop for you upon exiting it. And then there's a small hint of a genre-appropriate weapon, upon this cheerful shopkeeper's person, either espied beneath the folds of clothing as he leans across some old crate to adjust a display, or else flashed conspicuously, with a frozen smile the moment you make a less-than-friendly move of your own. Perhaps if things progress, the 'kindly' and venerable vendor will make a sharp whistle and suddenly several younger-clones will appear, attired in similar cloth and hatwear to enhance the family resemblance but wrapped around/sat upon bulkier frames, augmented with more obvious armour they might have picked up along the way and holding their possibly unorthodox items of weaponry from the off. With an open-handed gesture you attempt to calm things down, or else take it the other way, because you're a Big Goddam Hero (but obviously not above trashing a store), or at least
think you are, and who knows when and where you next wake up.
But it's not like that. Yet.
At best, expect the Depot to be empty trestle tables, perhaps some loose canopies splayed across the area, between the five columns that corner and centre the plaza. Things may be tucked under the tables or litter the walkways between. The mobile traders that arrive known which things they laid on the tabletops, and your overseer knows what has been brought up to lay alongside them. The chief fort-trader and the chief caravan-trader then walk up and down, tapping items of theirs and their counterpart's, indicating a perceived (or suggested) equivalence, each keeping an internal tally that they try not to reflect
too accurately in perturbations to their poker-faces. Smiles may erupt if a bundle of items are hoisted up and carried over to the trading-train, unbidden, or things can sour. Items may arrive to be sold during proceedings, there is always space, and some things can be taken away to wherever it is localky stored. If things continue well, uninterupted by rudeness or raiders from outside, the tables will be removed of all-and-only those items now commonly agreed are the caravan's to take, the rest are dealt with whenever someone finds the time.
(Welcome to the inside of my head. It's quite roomy in here, but a bit noisy too.)