My understanding was that breast milk (at least in humans) gave the baby antibodies, but not the ability to create those antibodies. So, the effect wouldn't last.
But still I would imagine that such antibodies would be exponentially more valuable in the earliest moments of life, where it’s likely that the newborn fist comes into contact with the mother’s fecal material and all of the bacteria living on our skin.
Some theorize the baby needs the mother's poop, to start it's own digestive microbiome. It works that way in other species, but I don't know if it's more than speculation for humans.
You also need a skin microbiome, but you can get that later.
Humans produce colostrum early after birth as well. There's a practice of saving it if the mother produces enough milk in case the newborn later has an illness and could use the antibody boost.
That’s correct - one of the proposed treatments for coronavirus is synthetically generated antibodies for seriously ill patients; it won’t teach the immune system as you said but reduces viral load.
This is what I believe to be the case too - so-called "passive immunity" gained by just having their mother's antibodies from either breastfeeding or even earlier via the placenta (at least for humans - as I understand it not all mammals do it via the placenta?). Eventually I think this protection wears off, but can be topped up with further breastfeeding, or eventually the baby starts to generate their own antibodies
