There's a post on Reddit describing a custom solution:
https://www.reddit.com/r/Starlink/comments/sb4dei/homebrew_poeethernet_adapter_for_rectangle/

On Mon, Apr 18, 2022, 7:09 PM David Lang <david@lang.hm> wrote:

> gien that the new dishy has the power supply built in to the router, an
> inverter
> is really the only option.
>
> I just picked up a cheap 300w inverter to use to power my dishy, but
> haven't had
> a chance to try it out.
>
> David Lang
>
> On Mon, 18 Apr 2022, Bruce Perens wrote:
>
> > I have rectangular dishy here in Berkeley where I can't test it, because
> > we're not a supported area yet. Dishy is going to Macdoel, California,
> off
> > of the grid, to run an SDR transceiver on 10 acres where I can have any
> > antenna I want. There are currently "1200 watts" of solar (derate that to
> > 25% for practical use) and a bunch of lead-acid batteries in a 48V
> system,
> > inside of a hi-cube freight container.
> >
> > Currently my plan is to plug the router into an inverter. The one on hand
> > is pure sine, but I don't expect Dishy to care. Switching power supplies
> > generally have a wide voltage range and are independent of wave shape or
> > frequency or even whether the input is AC or DC.
> >
> > I'd be interested if anyone else has had to produce off-grid power for
> > Dishy, and how they have done it.
> >
> >    Thanks
> >
> >    Bruce
> >
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