This is an area where language is changing fairly rapidly, so the answer is a bit complicated. I will do my best to address this question from the purely "non-political" angle of how is realistically best to use this term appropriately for someone whom English is a second language, rather than address any larger philosophical point about the word.
There really are plenty of cases in the English language where the term "baby" can be slipped into in a fairly innocuous, non-offensive way. For instance, if you're about to go on vacation and you say "I'm going to Vegas, yeeeeah baby!", it'll generally be perceived as though you're making kind of an exaggerated statement expressing excitement. In this sense it isn't really perceived as though you are directing the term toward the other person at all, but rather that you are just reciting a kind of mannerism people use when they're feigning excitement, or you're playing up a certain character.
Second, there's the standpoint of using the term "baby" in slang as a pet name, or in an "amatory" way, to refer to a loved one in a relationship. When it's used in this way it's gender neutral. Again, from the standpoint of someone trying to learn to speak the language, you ought to know that the use of the term "baby" in this sense is, at least in 2023, extremely common - in thousands of song lyrics, screenplays, and so on - and not generally seen as unusual.
Third, there are also certain circles or subcultures where the term "baby" can also be loosely used in general when addressing people, usually friends but possibly anyone you are friendly with, in a sort of endearing way. This is not super common as a slang term in so-called "General American English," but there are certain subcultures or dialects where the term will be used a bit more freely in this way. As you note in your link above on slang in the jazz community, the term has a history of use in African American Vernacular English, particularly a few decades back. It certainly isn't exclusive to AAVE though - for instance, in my experience, a lot of the older Italian-American folks living in Philadelphia, typically women, will throw this term around quite a bit, along with the ubiquitous "hun", which has become kind of a shibboleth for the Philadelphia dialect. There are no doubt countless other subcultures or dialects where the term is used a bit more loosely in this way. All of these things have kind of drifted in and out of style in the last few decades as societal attitudes have shifted.
If you are learning to speak the language, you should be aware that this particular sense is kind of a "risky" use of the word "baby." Its appropriateness varies pretty significantly depending on the specific dialect, subculture, or context or setting you use it in. Calling someone "baby" in the wrong situation can certainly be seen unintentionally as sexist or demeaning. In general, unless you have an intuitive sense for when it is appropriate to use the term this way, it is probably best avoided. Certainly it should be avoided in any kind of workplace setting, for instance.
Lastly, there is the kind of very modern political idea that we should try to examine or deconstruct the foundations of the English language itself to understand and better identify sources of sexism, racism, societal bias, and so on. Some people have more radical views on this sort of thing than others, and it remains to be seen how it'll shake out. I've seen people object to the use of the term "baby" as a pet name, for instance, suggesting that it's infantilizing. However, at least as of 2023, the term remains in pretty common use in this way. (And even in some of these more radical circles, I haven't seen anyone suggest that "I'm going to Vegas, yeeeah baby!" would be a sexist use of "baby," as it just seems to have a different interpretation.)
