JWST was captured 4 days after launch on a 17" telescope, when it was just beyond the Moon's orbit (or about 1/3 of the way to L2).
https://www.virtualtelescope.eu/2021...s-29-dec-2021/
They estimated the Visual Magnitude to be about 14.7 - but at that time, the sun-shield was not fully deployed. The fore- and aft-pallets were extended full-length, but the kite-shaped sun-shield had not been spread out laterally.
Now that the sun-shield is fully deployed, the reflected sunlight should be at least 3 or 4 times more than its configuration at the time of the Day 4 capture (roughly 1 or 2 magnitudes brighter, say) - but this will be offset by the receding distance.
It is currently about twice as far away as at Day 4, leading to a 4-fold reduction in apparent brightness (about 1.5 magnitudes, say), which should be pretty much compensated for by the increased reflective area. When it reaches L2, it will be roughly 3 times as far away as at Day 4, which would be roughly a 10-fold reduction apparent brightness (about 2.5 magnitudes say), but again, largely compensated for by the bigger reflective area.
In summary - I would guess you'll be looking to capture a Magnitude 14 to 15 object (or thereabouts).