Eberron's connection to wildspace was never defined in canon.
Spelljammer ended with AD&D 2e, while Eberron made its debut in D&D 3.5, with the result being that the two settings have little overlap. Eberron couldn't have been mentioned in an AD&D Spelljammer book, and I don't recall any mention of spelljamming in any Eberron book.
The closest I can find is the Dragon Magazine #339 article Races of Spelljammer: Wanderers of Wildspace, published January 2006, meaning it is a rare D&D 3.5 Spelljammer source produced after the release of Eberron, and during the period when Dragon content was stated to be official. The article states:
Many Wildspace races build and maintain their own spelljamming vessels and most can be encountered on groundling worlds either openly or in secret. Any of these Spelljammer races might also serve equally in a campaign based in the Forgotten Realms, Eberron, or any other crystal sphere.
This suggests that Eberron's solar system is at least in a crystal sphere, meaning that it's somewhere in wildspace. D&D 5e says that all settings including Spelljammer are part of a unified D&D multiverse, but doesn't describe those interconnections in terms of crystal spheres or wildspace. Spelljamming ships and Realmspace are described in D&D 5e's Waterdeep: Dungeon of the Mad Mage, so we know they're still a thing, but except for that one Dragon article in issue 339, there have been basically no mentions of wildspace or crystal spheres since D&D 3e launched in 2000.
We know at least that Eberron is unlikely to receive frequent visitors from other worlds, as far as published material goes. Visitors from other material worlds aren't mentioned, unlike, say, Greyhawk and the Forgotten Realms, where Mordenkainen and Elminster have visited each other's worlds. You don't have firearms in Eberron, even though those are available in Wildspace and the Toril. We might deduce that Eberron's solar system, if it has a crystal sphere, doesn't appear to be easy to find or travel to.
There was a Spelljammer article for D&D 3e in Dungeon #92, but it only covered one solar system and not between-setting travel, and stopped just short of retconning crystal spheres out of existence. Spelljamming ships are mentioned in 4e's Manual of the Planes, but they work by plane shifting instead of actual spelljamming travel.
There was a 2004 article, Planes and Adventuring, which asserts that Eberron's planes are connected to Eberron only, and that Eberron is not connected to the Great Wheel. It doesn't cover the possibility of transport between Eberron and other material planes.
There is an forum thread on this topic, but naturally it's homebrew material rather than official. According to a Candlekeep thread, Elminster once visited Eberron in the Stormreach video game, and Eberron author Keith Baker says there is no official status for Eberron in the Spelljammer cosmology. A poster on that thread believes that crystal spheres were a definitive part of the 4e planar cosmology, but I don't believe that's canonically the case in 4e lore.
In a tweet, Eberron creator Keith Baker gives his opinion that travel to or from Eberron is entirely up to the DM:
Ultimately, travel to/from #Eberron is as easy or difficult as you want it to be. If you want House Orien operating portals between worlds, it’s your story! Or the arrival of the warforged in WD could be a mystery; they don’t know what brought them to Faerun or how to get home.
The 3e Manual of the Planes, p.44, also notes that travel between campaign settings is possible via the Plane of Shadow (5e calls this the Shadowfell), a shadow portal, a demiplane connecting the two worlds, a planar cataclysm or accident, or a portal. The 4e Manual of the Planes leaves the existence of crystal spheres up to the DM.
The D&D 5e Eberron Rising from the Last War, p.228, asserts that while Eberron is part of the Great Wheel, it is also disconnected from that cosmology, which is consistent with earlier conceptions of Eberron's planar cosmology. On page 232, "Eberron and the Multiverse", it suggests that this is because the progenitor wyrms created Eberron from scratch and deliberately hid it in the Deep Ethereal, and that it can be theoretically visited this way, though with difficulty. The Ring of Siberys forms a barrier, not unlike a crystal sphere, though crystal spheres and wildspace are not mentioned. Whether this barrier is absolute or weakening is left up to the DM.