Related to this is Loeb's proposal to nudge the Juno spacecraft, currently orbiting Jupiter and soon facing EOL, into the path of 3I/Atlas to try to scan it and snap some pictures. I doubt it has enough fuel left, but I hope they're looking into it.
I suggest you read the paper. It's packed with subjective language (Row one of table one, the incoming trajectory is said to be "virtually" in the ecliptic plane), and has so many unstated assumptions behind their so-called significance of the trajectory it's not valid.
And the stated 5 degree angle disagrees with published observations.
And the estimate of the size is over double the confirmed observations of size.
While "Not aligning with scientific consensus doesn't make your suggestions worthless" is true, ignoring published results does.
If the probe doesn't have enough fuel to leave Jupiter's orbit, we get a better view of it from here with our much bigger optics.
Sure, the closest approach of 3I/Atlas to Jupiter is 53.56±0.45 Gm, the closest approach of 3I/Atlas to Earth is 268.98±0.3 Gm — but we have more and better sensors down here.
For photographs in particular, Juno's JunoCam is spectacularly bad, because "it was put on board primarily for public science and outreach, to increase public engagement, with all images available on NASA's website" — while it can be used for actual science, at the orbital apsis (8.1 Gm) it has a worse resolution, when looking at Jupiter, than Hubble gets of Jupiter from LEO (a distance of ~600 Gm for https://esahubble.org/images/heic0910q/).