Your powerful spellcasters have several options for attending distant auctions, which each have their costs and benefits. However, I'll first comment that the options you presented are not particularly viable. Astral projection will only work if the auction takes place on the Astral Plane, which is rather unlikely. Sending stones can only be used once per day, which is ineffective for an auction. But there are plenty of options which do work well.
If your bidder is within 500 miles of the auction, then they can cast project image, a 7th level spell which projects an illusory version of yourself to somewhere within 500 miles. You can use the illusion's senses and speak through it, almost as if you were actually there, and other people also see you as present. This spell has a duration of Concentration, up to 1 day, which is enough time to not only attend the auction but to also do talking and inspecting before and after the auction. This, I imagine, would be the preferred option for spellcasters who are within range.
Scrying and Sending
If your bidder is more distant, then combining scrying and sending is an option. Scrying is a 5th level spell which requires a 1000 gp focus, which is within the means of a powerful spellcaster, and it allows the spellcaster to see and hear a particular creature or location anywhere on the same plane of existence. This will allow the bidder to watch the auction in real time. When the bidder wishes to make a bid, they can cast sending (a 3rd level spell) to deliver the bid to the auctioneer.
While this option has unlimited range, it has some disadvantages. Scrying takes 10 minutes to cast and it has a duration of up to 10 minutes. This means you need to know beforehand with reasonable accuracy when the auction will start (this can be achieved with sending) and you will have problems if the auction lasts longer than 10 minutes. Additionally, you have to use a 3rd level spell slot or higher for every single bid you make, which may be inconvenient for a lengthy auction.
Teleport or Teleportation Circle
Powerful spellcasters don't have to settle for remote communications if they don't want to. They have the ability to travel anywhere they want instantaneously. Thus, physically attending a distant auction is an option available to them.
Teleport is a 7th level spell which allows the caster to transport themselves (and up to 8 associates) to any location on the same plane with which they are familiar or at least have a good description of. However, unless they have an object from the destination or there is a permanent teleportation circle nearby, there is a probability of arriving off target which is a risk which may or may not be acceptable.
Teleportation circle is a 5th level spell. It will only work if there is a permanent teleportation circle near the auction (what 'near' is depends on how far the bidder is willing to travel by non-teleporting means), and it consumes 50 gp of material components, but it carries no risk of mishaps and is available to mid-level casters.
Telepathy or Voice of the Chain Master
This option requires the caster to have a trusted hireling or associate physically attending the auction. Telepathy has unlimited range and a duration of 24 hours and it allows the caster and target to share words, images, sounds, etc. instantaneously. This will allow for the caster to observe all that is happening at the auction and be able to deliver instructions in real time to their associate who will make bids on their behalf. Note that telepathy can be cast at the target from any range.
A similar option available only to warlocks is the Voice of the Chain Master Invocation. If a warlock with this invocation sends their familiar to the auction (by any means), then the warlock can observe what the familiar observes and speak directly through the familiar. However, sending a familiar over a long distance may be non-trivial, although retrieving the familiar is as simple as dismissing it (action) and causing it to reappear (another action). One advantage of this option is that it is available at only 3rd level. This will likely only be used if the warlock is within a few hundred miles of the auction, close enough for a bird familiar to fly there in reasonable time.
Crystal Ball of Telepathy
This legendary magic item allows the bearer to cast scrying and communicate with telepathically creatures within 30 feet of the sensor. This comes with the time limits of scrying but avoids the costs of repeated castings of sending. A legendary magic item is a high price to pay for this luxury, but for an exceptionally powerful spellcaster it is a worthwhile investment.