Oh, here is a quirky but interesting idea.
SAR is really taking off as an intelligence gathering capability provided to customers by businesses. In visible light we have the model of Planet Lab providing a rich array of data products at various pricing schemes, in SAR there are several companies starting to do the same. Consider Capella Space and ICEYE and Umbra (also) for example, and even NASA + ISRO joint projects.
In other words:
There's an ever-increasing number of radar flashlights lighting Earth 24/7!
Perhaps a modest, low cost project can be envisioned that parasitically makes use of whatever SAR beam happens to be hitting a patch of ocean.
Fishing boats contain metal surfaces that can sparkle when illuminated by radio.
Stealthy aircraft avoid 90° internal corners for their propensity to reflect directly back towards the transmitter, but once you relax that condition and receive from a substantially different direction than the transmitter, all bets are off. Now, all kinds of random configurations can have unexpected bright reflections (high radar cross sections) at certain combinations of incident and reflected directions relative to the object.
So for an ad hoc suboptimal but low(er) cost ship presence detector, why not use the reflections produced by other SAR satellites' powerful beams?
We know where both we are and where those are at any moment via TLEs to better than 10 km and we know were most ships are via AIS, so knowing the shape of the Earth and having a delta-t (difference in arrival time) between a weak direct beam and a reflection should allow us to start to reconstruct the positions of the reflections.
It will take some pattern searching to match up constellations of ship reflections to known AIS positions, but these techniques exist (cf. How (the heck) does Astrometry.net work?) Any reflection that doesn't match up with AIS positions is a candidate for further investigation.
SAR beams are certainly mostly focused on the target scan area, but any antenna will have all kinds intensity below -60 to -90 dB in all directions, which will be a similar intensity to weak reflections of the primary beam.
This will take some serious development, but it really could work!
From Star-shaped artifacts in SAR images of the "Suez Canal traffic jam seen from space"
Source and original ESA source
From Spacenews.com's SAR Renaissance: Pandemic slows but doesn’t stop constellation progress: