I recommend basing this off of DM-28542, in which case you can just use

uniqueChildren = catalog["detect_isDeblendedPrimary"]

which will give you the unblended isolated sources and the sources from blends with >= 2 children, without any of the restrictions on patch or tract.

Indeed, I will implement the above once DM-28542 lands and is part of a weekly RC2 processing.  This point here is to try to get the best set of flags we can based on catalog flag entries prior to that ticket getting merged.  To this end, I have updated the sky source selection to only use the non-model isolated scarlet models via a selection on the sky catalog of:

skyObjCat["parent"] == 0 & skyObjCat["deblend_nChild"] == 1

.  In my first pass at doing this, I noticed that the outer "ring" in the COSMOS 9813 tract was getting selected against.  These are the sources without full-band coverage and, if I understand correctly, scarlet falls back to the effective "no model" measurement style for these objects.  They get the "deblend_skipped" flag set and can be identified in a sky object-only catalog in that they all have:

skyObjCat["parent"] == 0 & skyObjCat["deblend_nChild"] == 0

so I add these back in. Comments in the code have added to make note of this.

The sky object plots do indeed now look much closer to what we were getting with meas_deblender runs. However, there are still offsets to more positive sky measurements in the circular aperture measurements as demonstrated in the following plots:
w06 scarlet:

w06 scarlet this ticket:

w02 meas_deblender:

So, while things look much better, there is still a bias towards higher sky levels in the scarlet no-model plot compared to that of the w02 meas_deblender run.

To rule out the possibility of differences in source placement somehow creeping in, I made plots comparing them between the scarlet-base w06 run and the meas_deblender 02 run. Some examples:

Identical:

small differences:

They are nearly identical (first plot), but with the occasional exception (second plot). I believe these small differences stem from small differences (in particular in the fgcm calibrations) at the visit level stage, leading to slight differences in the mask planes used for source placement selection (and has nothing to do which which deblender was run).
More examples for all patches in tract 9813 can be perused (for some finite amount of time!) here.

So, it seems there is still something "different" about what is getting passed into the measurement algorithms (perhaps a combination of Fred Moolekamp + Lee Kelvin could file a ticket to look into this in more detail?)  Totally naïve speculation: are the boxes big enough (but...if not, should the algorithm fail/report NaN for flux?  Most entries have the circular aperture flux flags set for both deblender outputs).

Ok, now for the main catalogs, I have gone with the approach of including scarlet-model based versions for both isolated and blended sources, whereas RFC-750 concluded that the isPrimary sources should include the non-model versions for isolated sources.  The reason for this it that I can't uniquely select the isolated scarlet-model sources (in order to swap them out for the non-model ones).  This is due to an error in the propagation of the "deblend_parentNPeaks" flag in current catalogs (this will also be fixed on DM-28542).  I have kicked off a runs of all RC2 tract/filters with the current selection.  Only the 9813 HSC-I is done so far (the others are waiting in the queue), but results will be tricking in here.  As an example of why I think I've potentially got this right, look at the footprint distribution from the original w06 run:

vs. the one from this branch:

Note that the latter is missing the extra "branch", which I am assuming is attributed to the non-model isolated "leaf".

Would you mind giving this a look to make sure I have the logic of the current scarlet flag setting correct and that this is the "best" we can do at present for looking at consistent samples.  This is meant as a stopgap until we can do this "properly" after the changes in DM-28542 make it into an RC2 weekly processing run).

Looks good, just a few comments in the PR.

Thanks, Fred. As to your main comment on the PR, yes, I did look at the distributions omitting the skipped sources. There are differences (of, course), but they do not explain the trends noted above. Here is the histogram plot:

and the sky distributions for:

meas_deblender:

scarlet skipped excluded:

scarlet skipped included:

The “included” sample seems like the fairer comparison to me, but I’d be happy to leave them out if you fell strongly about it.