This is one of the more difficult questions to answer... In my opinion it all really depends on the story that you want to write, and then also understanding that a reader's immersion in your story is sort of dependent on being referential to experience. You either have to be able to write things in a way that relates to the real-world, or you have to put in the leg-work with your world-building so that your story can be self-referential and readers will still understand things.
So, I would say that writing a rom-com story where the entire plot is very mundane and non-technical could be written entirely without research, relying only on experience and gut feeling (which is sort of how approaching new relationships works in real life anyways...). Although I have heard stories from slice-of-life and romance writers who frequent cafes to just sit and people watch for inspiration, so I guess that's some form of research?
Then you have stories that revolve around some level of technical expertise with concepts that people can relate to - ranging from cooking a series like Shokugeki where I think it would be important to know ingredients and cooking techniques, and then maybe going as far as flavour combinations, to a martial arts series where an understanding of techniques and body mechanics is definitely at the fore, but past that maybe even an understanding of the philosophy and history could be really important to grasp. Readers, don't necessarily have to have directly experienced these activities, but they will have experienced relevant things that they can relate to the story with, such as tasting and moving their body. So as long as your story doesn't contradict their informative experiences, then you can get away with doing less research, but I honestly feel that the more that you yourself know as the writer, the deeper you can go with your story and the more immersed and engrossed you can get a reader.
A step further in my mind is then understanding more complex and multifaceted fields that an average reader will be less likely to be able to conceptualize or relate to. These encompass areas of science, culture and history. Here you become the temporary voice of authority on the matter, and in general if you are going break the rules for the sake of your story then it's usually best to know them well first... This is how series like The Expanse and The Lord of the Rings are so beloved by fans. It is also kinda dependent on the tone you set for your story also - if you start out promising something hyper-realistic and then pivot into something that is implausible or false then you will cause a dissonance that will not sit well with readers. Anyways, this is the category that I believe requires the most research, and then a lot of good world-building to establish rules for the reader to relate to. Sci-Fi is a good example of this as a genre, encompassing a lot of more conceptual and speculative story ideas to do with spacefaring, dystopias, A.I.'s etc for which the general reader will not be able to directly or even indirectly relate to in most cases, but then the writers create consistent rules that they can hold on to. If we then compare Star Wars to Starship's Mage to The Expanse, I would say that space travel and combat is the most unrealistic and worst thought through/presented in Star Wars, and although this doesn't stop it from being an enjoyable story I definitely appreciate the other better established systems much more. Good research in these fields helps to add depth, cohesive world-building, and remove inconsistency in your universe and plots.
Honestly, I think that most stories will never be just one of these levels, and require circumstantial levels of research at different points...
I'm kind of on the fence on how much research needs to be front-loaded though... part of me feels that you may be able to get away with writing first drafts without and then fleshing things out once you have the skeleton of a story... but then I really think that it's not efficient or even beneficial to work that way; surely you want to build on the strongest foundation possible from the start in almost all situations right?
I always find myself doing a ton of research one way or another. The only time I don't research is when I'm just writing down story concepts or when I already feel confident enough in my knowledge to write without it. For instance, I did no extra research when writing the Necromancer piece I released for Halloween last year, but I have a decent enough grasp of medieval fantasy, and fantasy necromancy as a concept, through extensive reading of book series, and exploring similar characters and concepts through D&D. I think that it's important to realize that your experiences with consuming media such as manga and comics and books and TV and Movies and games is all a form of research also - but, as you say more inspirational or influential as opposed to concretely informative.