The mechanic of Companion presents multiple questions, related to the multiple parts of the mechanic:

A Companion is cast from outside the game; Does Oathbreaker allow this?

Under the existing rules, Oathbreaker has no sideboard and abilities which refer to outside the game do not function. While Commander also has the same rules affecting this, we don't believe accommodating this mechanic is the correct course of action. It would bring into question things like burning wish [] that we have already decided are not in the best interest of the format as having an explicit deck size that all players must work with is one of the core parts of the Oathbreaker format. Adding a sideboard or wishboard of any variation breaks from that symmetry of what players bring to the table and allows for 'silver bullets' to be safely accessible to the decks that can access them without drawing them at an inopportune time.

Companion cards require a deck building condition to be met; How difficult is it to meet these requirements within the existing requirements of Oathbreaker?

The companion requirements vary greatly between free and impossible to achieve. Lutri, the Spellchaser [] (U/R) has a restriction already in place by the singleton nature of the format. Kaheera, the Orphanguard [] (W/G) and Zirda, the Dawnmaker [] (W/R) are fairly easy to satisfy as they only have restrictions on a subset of the deck. (R/G), Keruga, the macrosage [] (U/G), Obosh, the preypiercer [] (R/B), Gyruda, doom of depths [] (U/B) have restrictions that are difficult to achieve without creating a significant disadvantage. Lurrus of the dream-den [] (W/B) and Umori, the collector [] (B/G) are (currently) impossible due to existing restrictions within Oathbreaker deckbuilding. The only unknown is the W/U companion, but with the currently revealed cards we can already see a large imbalance on which color combinations benefit from this mechanic within the context of Oathbreaker.

The cards with Companion are creatures with abilities; How impactful are these other abilities?

The above mentioned companion creatures are the only ones currently available to us, and while they all have cool and exciting abilities beyond their namesake mechanic, none are expected to warp the format from within the deck.