The prohibition of hand-washing for a child in the prohibitions of the elders

Hello Rabbi,
It is said in the Torah, “You shall not eat them, for they are an abomination,” and the Gemara requires this: “You shall not eat them—you shall not feed them, to warn the great over the small.” The Gemara’s intention is to say that the great is warned by the Torah not to feed the little one with anything that is forbidden, meaning that he should not feed them with his own hands. And the poskim have taken the view that this ruling on the prohibition of sifiya is not stated only in the prohibitions of eating, but also in the other prohibitions of the Torah. I saw that the poskim have taken the view that the prohibitions of Shabbat are also included in the prohibition of sifiya (although there is no explicit source for this in the Gemara). I wanted to ask you whether it is appropriate to divide here between the prohibitions of Haftza and Gebra. In other words, the verse spoke about the prohibitions of eating (the prohibitions of Haftza), so it is natural to expand the prohibition to all the prohibitions of Haftza, but where does it come from to expand it to the prohibitions of Gebra as well?
Best regards,