Like Searle's Chinese Room thought experiment, you are relying on human intuition as to what can and cannot be sentient, which ultimately is boiled down to how like you something is. You readily recognize sentience in dogs that can't hold lucid and eloquent conversations with humans because they are biological beings with brains and hearts and blood and guts like you and me, not for any objectively measurable ability to demonstrate "intentionality" or "internal state of mind".
On the other hand thinking a simple data storage structure is sentient merely because it's big doesn't sound very compelling. You think the sentience of a dictionary depends on its size or the words you store in them? A phonebook of the United States is ten times more sentient than one of Spain because you can retrieve more data from it? If you walk into a warehouse does the warehouse become sentient?
You're right that it's exactly like Searle's Chinese Room experiment because Searle was and is correct (and people stil horribly mangle and misunderstand his argument), functionalism is silly. The mechanical turk can play chess better than my cat but is neither sentient or even intelligent, it's just the most proximate machine you interact with.
It is very convenient for us to say that only things we can recognize as being like us deserve to be called sentient, because that means we do not have to consider them anything more than a tool. Historically human beings have applied this to animals and even other human beings. It is neither a scientifically nor ethically justifiable philosophy.
The only reason it's different from any other function is because the output is nicely stated prose that causes emotional reactions from the reader. If all did was output an integer, we wouldn't be having this conversation. But because humans have a deep sentimental attachment to language, we are fascinated by something that can produce it.
When DALLE 2 creates a new image of an entirely novel scene, is it just copying and pasting? Of course not. It is distilling and reasoning in concepts. You can’t escape that. GTP and friends are doing something similar. Brushing aside these astounding strides as statistical tricks of the eye is stupid. Clearly these training algorithms are discovering things that are much deeper. There’s no reason to think sentience has been achieved but you are absolutely fooling yourself about the nature and trajectory of these programs.
Imagine instead of lambda or gpt-3 we take ten thousand years to walk through every possible conversation manually, write down and assign a percentage to every possible branch of conversation in a hash table. Call it the world's slowest, bootleg neural net. Is the hash table API sentient?
We perceive a dog to be sentient because it has intentionality, self-awareness and something resembling an internal state of mind, not because it can talk or not. Even a snail is more sentient than a chatbot.