Unless they subsidize, New Glenn will have to be quite expensive. As the announcement says, they spent 3.5 billion just on a factory and a launchpad, and they are years away from launching.
Amazon, as such a high visibility public company, may have a hard time justifying a 2X+ price difference versus launching on Falcons, and for Starship the difference could be significantly more.
It's also questionable if Amazon is willing to wait 3 years to get any significant amount of sats into orbit. That will give Starlink a big advantage.
Of course SpaceX also has an incentive to delay Kuiper, so they might not bid for it at all, or only provide very limited availability.
The money has to come from somewhere.
Either it's from Bezos, or it's from launches with a price that won't make it easy to win many customers in the very small market of large payloads.