Would a person go to jail for this?

I think you have more plausibility problems than the legal outcome of the baby's accidental death. Firstly, it would be a very strange glass pitcher than would shatter into small shards when dropped from hand height onto a table. Secondly, if the baby being fed with a spoon, that spoon is necessarily a small one and a piece of glass large enough to harm the baby might well be noticed. Thirdly, young children and, sometimes, older children and adults may swallow toys, coins, safety pins, buttons, bones, wood, glass, magnets, batteries or other foreign objects. These objects often pass all the way through the digestive tract in 24 to 48 hours and cause no harm. However it can happen. The damage is likely to be from choking rather than cutting. As for the legal consequences, in my local jurisdiction (England and Wales), for one or both parents to be successfully prosecuted following a baby's death, a consistent pattern of serious neglect would have to be established by the prosecution side in court. An example might be drug users who left pills within reach of a child old enough to feed themselves, and then failed to adequately supervise that child. By the way, nobody seriously uses "unbeknownst" these days.

Thank you for your reply. I'm wondering if this would be more realistic:

When the pitcher shatters, one of the shards of glass lands on her son's tray right in front of him. While she's cleaning up the mess, he swallows the glass shard.

Where I live, prosecutions after a baby's accidental death are rare unless it is clear that serious neglect has taken place. For example, the mother knew the glass was reachable by the baby and did nothing, or the baby started choking and she did not call for help. A baby' accidental death is a very sad thing, and the prosecutors would ask themselves if a prosecution was in the public interest, and for that standard to be satisfied, a very serious pattern of neglectful or abusive behaviour would need to be established, e.g. past injuries, broken bones, etc revealed at post-mortem.

I would add from an American legal standpoint (I'm a retired lawyer but man oh man it's been decades since I handled a criminal matter), generally the parents are the first persons of interest when an infant dies, with the secondary person of interest being a babysitter or nanny (but a live-in like an au pair would probably be on the first level of persons of interest).

This does not mean a parent is always arrested and charged, but they are always of interest because they have the most access to the child. In particular, when it's a very young child who does not go to school, and maybe not even to day care, the parents and the child's pediatrician are the stars of a very small group of people with access to the infant.

So Mom would likely be questioned, and probably extensively, about the child's death. Police and the DA's office try to be sensitive to grieving parents but at the same time there is a very strong interest in getting justice for a murdered child and in getting a child abuser/killer off the streets. Hence they might be pretty gentle with their questioning, at least at first, but they will still go through the questioning process.

The (British) Association of Chief Police Officers has publicly available protocols for investigating Sudden Unexplained Deaths of Children (SUDCs)