Your assumption is that the Bifrost requires a projection system. It appears that way because Asgard only wanted one way into and one way out of Asgard. It is also likely the users of Dark Magic are limited or it requires great skill or personal power to utilize the Bifrost portal creation magic without technological support.
The Marvel Cinematic Universe Wiki defines the Bifrost as a type of energy:
The Bifrost Bridge is a dimensional energy which allows instantaneous travel to any planet. It was used primarily by the Asgardians, who were able to use a Rainbow Bridge to harness the energy and access the Bifrost in order to travel to and protect the Nine Realms.
The Bifrost was also able to be called upon using dark magic and was also imbued into Stormbreaker, allowing its wielder to access the bridge at any time. The immense dimensional energy, given enough concentration, could also be used to destroy planets.
The Bifrost isn't a thing, it is a technology/magick usable by people versed enough or powerful enough to create the portal (Einstein-Rosen bridge) between worlds. The power to bridge between worlds was an aspect of Asgardian magic (called Dark Magic) which was channeled through members of the Asgardians capable of utilizing it.
Odin using his personal energy stores and Heimdall who was also able to summon such magic, in extremis. Since Heimdall was one of the Vanir, the gods of Asgard associated with magic, it doesn't seem unreasonable he could summon the ability to create a portal between Earth and Asgard using his own personal energy.
The technology of the Bifrost system however meant no Asgardian had to tap their personal power to do so. Like all technology, the goal was to simplify their need and make it able to be done even if a user of Dark Magic wasn't available. All you needed was the key -- which was Heimdall's sword.
It should not surprise anyone that Stormbreaker can be enchanted to do this. In the comics, Thor's Mjolnir was also capable of creating bridges between worlds and teleporting Thor to Asgard, as needed. In Avengers #166, Thor tries to create a portal to teleport the now super-powered Count Nefaria to another realm of existence. Nefaria counters by choking off the portal with a skyscraper.