Free chlorine can obviously damage gills, but small amounts of bleach in a tank don't have to be a problem. Your source describes permanent exposure at a measured concentration, but if you dose a
theoretical amount of "0.1ppm free chlorine" into your tank once, a good part of it reacts with organics and trace elements before it reaches the fish.
"The recommended safe long-term exposure level is total chlorine < 0.003 ppm (ANZECC, 2000). Total chlorine levels ≥0.1-0.4 ppm have been associated with fish kills (Langdon, 1988) for freshwater species and ≥0.128-0.250 ppm for marine species (ANZECC, 2000)." - Page 193 (105/123 in
your PDF)
0.02mL of 8% bleach in 50gal is only about 0.01ppm free chlorine, so below the levels that actually killed fish in the linked article, but above levels that would be considered safe during long-term exposure.
Bleach dosing is a thing... It's certainly weird and I wouldn't recommend it, but it's a thing people do. Bleach reacts quickly with organics and trace elements, so free chlorine drops fast. It does form some nasty compounds, but it won't nuke the tank when bleach is allowed to drop to safe levels again, so I think your shipment had other issues

.
Many people here clean their filter socks with bleach and put them back in the sump unrinsed. A decently sized tank's chlorine demand should be high enough to handle it. So I don't think you accidentally killed your shipment with a few droplets and OP has no reason to worry about a tap-water-rinsed pipe
The 0.02mL figure is around the 10ppb=0.01ppm lower end of what that report had. I calculated that number for illustrative purposes and included it in my explanation for a reason. The report included two case studies, one freshwater and one saltwater.
"Case 2: chlorine 0.01 - 0.05 ppm and pH7.28 – 8.14." (Page 194, 106/203 of the PDF)
Your quote is from their introduction to pathophysiology of chlorine exposure, not what they actually reported for their case study. They do structure their report a bit oddly though, so you do need to read the entire section to understand what they mean. A total kill would also start at 0.2mL in 50 gallons, not a lot of liquid either.
The dosage is also not for permanent exposure. The EPA says 13ppb free chlorine in saltwater is the acute exposure (1 hour) limit. Their chronic exposure (4 days) threshold is 7ppb free chlorine in saltwater.
https://www.epa.gov/wqc/national-recommended-water-quality-criteria-aquatic-life-criteria-table
Nevertheless, I do agree there are enough organics and random stuff in the water column to neutralize a good amount of free chlorine in a very short amount of time. I also disagree with dosing bleach since it produces too many very toxic compounds.
We also do use completely fresh tanks with just enough cycled media to do our conditioning of new imports, so free chlorine probably will last longer in our tanks, so my concerns may be overblown for the average reefer. Thinking about it more, if OP has enough stuff in the water column to support sponges, it probably is mostly a non issue.
I should note, chloramines are much more persistent than free chlorine. So if total chlorine is mostly chloramines, total chlorine concentration could remain higher for longer even in a dirty tank. Something to be aware about if doing large water changes in a city with chloramines.