> Would you characterize the items they hand to the court as similarly extreme in both ways?

It's really difficult to answer this separate from one's biases.

I'd also note that Trump, then Biden, then Trump again escalated the use of the shadow docket way beyond historical norms [1]. This was a deliberate choice by both Presidents.

> there is something fishy with both sidesing it

Didn't mean to both sides this, at least not at the level of the Court. The Court has had a conservative majority for a decade; one could argue Jackson and Sotomayor are balancing the court by leaning against its centre of pressure. But it's not unexpected for the Court to be a bit more deferential towards a Republican President. We haven't been appointing and confirming neutral arbiters for a while.

[1] https://en.wikipedia.org/wiki/Shadow_docket#Since_2017

> I'd also note that Trump, then Biden, then Trump again escalated the use of the shadow docket way beyond historical norms [1]

The President does not choose to use the shadow docket. The use of the shadow docket is controlled by the court justices, who (as you pointed out) have been a conservative majority for a decade.

You are correct that the use of the shadow docket increased under Trump and then Biden, but this is consistent with the (somewhat obvious) explanation that the conservative justices began to use this tool as a partisan weapon for Trump and the GOP and then later against Biden's policies.