Trade The incentive to trade, even among worlds distant to each other, is clear. The prime commodities are obviously be information, although a system rich in energy would crave matter and vice versa.
Routine trade missions would be nothing to send an average baseline on, it wouldn't be economical. Depending on the tech-level of the sender, everything from automated systems to dedicated AIs are feasible. Passenger liners would only exist in the most densely populated and politically stable regions.
Ownership The second problem lies in ownership. How can an off-system interest group secure long-time ownership, without having a substantial armed presence to back up their claim against political upheaval, or memetic totalitarianism?
One solution that was first developed in the post-Technocalypse period was that the traders there had no substantial assets in-system other than their know-how and temporary trading goods. But with the inevitably long view that comes from clinical immortality, the trading climate began to change. This led to longer and longer planning horizons. The rate of technological change had by now become fairly mild, with AI and immortals (or bionts with indefinitely long lifespans) around policies can be kept stable for centuries. Big profits were and still are made at the dynamic edge, but that is risky and requires something more like the know-how approach.
In the case of fast relativistic ships it is not even necessary to have indefinite biological life extension as far as the traders are concerned. A trip across the inner sphere may subjectively take no more than a few years, or even less - it depends on the efficiency and level of ultratech/transapientech/godtech drive technology. Often this is a lot more expensive and hence only used for special couriers, military vessels, and so on.
In any case life extension and/or government stability will be required for the planet or system-siders. The down side of this is that immortality often tends to breed complacency and other non-dynamic virtues. This leads to a lessening of new trade initiatives, and stagnation is the result. It is unusual however for an admin hyperturing to become complacent and ossified the way a biont who has had too much life-extension treatments might.
And when the statistical indicators become too significant to ignore, the downward trend is often unstoppable. And the statistical information, ironically, has to travel by the same routes as the trade goods they describe.
Long-distance Trading Beyond the Nexus (in areas like, for example, the Chronos Cluster, and also of course in the First Federation Era), a multistellar economy must depend on only speed-of-light communication and relativistic or sub-relativistic transportation. It is not unusual for the most routine business deals to take two decades for even longer, to be finalised between even 'next-door' neighbors.
Much depends here on the means of transport. If it is reasonably cheap (if slow) to send a few billion tons of water or a package of antimatter to another system, then trade will be possible. You need to have long-lived organisations on both ends, so that the recipient will be there once the trade is done. This is why the megacorps often became dynasties guided by their AIs in the first federation era, and why most clusters without wormholes need to have a stable planetary politics over centuries - if a planet changes too fast, few will want to trade goods with it. And it is important for property rights to be stable.
Information is another matter, of course.
Often much work has been and continues to be put into creating interstellar trade federations, simply to make it safe and profitable to trade. Overlapping such federations can stabilise whole regions, and transapient-led Empires in the core are of course ideal for organising and maintaining such things.
This factor was in fact very important in the development of the NoCoZo and also in the various trade organisations preceded it.
Moreover, even with the establishment of wormhole connections, there will always be a great many systems (the majority in fact) outside the nexus. And no matter how many stargates are made, as empires expand their interests further into the Outer Volumes, there will always be new systems being colonised (because population is always growing and the frontier is always expanding).
As far as the transapients and archailects are concerned however economics and trade is nothing but one more device they use for memetic manipulation, consciousness engineering, empire somatization, omnipresence by proxy, and whatever other things they get up to.
Opportunities on the Periphery With everything tied up and maintained by the hyperturing AIs, what's a poor nearbaseline (or a super-intelligent cyborg for that part) to do in the inner volumes? Granted, the archailects might work in mysterious ways, but the futility in economic endeavour for non-deities might be a large incitement for expansion and emigration. Better a ruler in hell, than a slave in heaven (Old Earth pre-singularity saying - origin unknown).
And in fact there are many who would rather rule in hell - they tend to be among the major immigrants to the periphery - all the idealists and religious extremists and guru cult-leader types and visionaries and prospectors (both freelance and corporate) and half-crazy types and whoever else is able to raise the capital to buy a relativistic ship and provisions. All this makes for an interesting periphery.
Megacorps, Foundations, and Institutes Perhaps the most resilient form of economic association known to mindkind is the Foundation. The strength derives from the fact that it has no members, only a charter that may be amended according to procedures and circumstances mentioned in the charter itself. Any profit made by a foundation is, once again, distributed by rules set forth in the charter. The only problem with this is that the foundation may survive its purpose. The problem of ancient foundations set up for some arcane purpose, (say to make definitive projections about the history of mindkind) is a very real problem the older the colonized worlds are.
A very few Foundations become Institutes, but many more simply continue, having outlived their purpose, and dragging the dead weight of the past along with them (such institutions could be found in the form of exoteric religions even in the pre-singularity age of Old Earth).