First I'm going to address one specific question which you elaborated on in comments:
Does not feeling the urge to pee before peeing mean that the child is not ready yet? And I couldn't find an answer for that, although reading everything I believe the answer to be: no, with good training almost "any" child should be ready.
Last part first: children come in all temperaments and abilities, and I would disagree that every child of your child's age can be or should be potty-trainable with the "right" methods. However, the literature does state that many children are ready to start toilet training by the age your child is now, and the vast majority by 36 months of age.
Many advocate the commando approach. I can see the positives in that approach; the child would definitely learn to associate a specific feeling (the urge to urinate) with the result (emptying one's bladder). Knowing that, I can see at least two outcomes: they dislike the sensation of urine running down their legs, and they learn it's better to let go on the potty chair, or, they don't care about the sensation and just pee at will, willy-nilly. (There are others in between the two extremes.) Because I didn't want to deep-clean my sofa, that was not my approach.
Is a child who cannot recognize the urge to urinate able to be potty trained? Not without a lot of parental involvement over a long period of time. However, if a parent watches a child carefully, they can recognize the onset of the recognition of the urge by the child's behavior, e.g. the child stops what they're doing, looks ahead blankly for a minute, then resumes what they were doing before (but with a wet diaper); the child clutches at their diaper or takes it off once they've wet it; some kids hide to pee or poop, etc. That's the child teaching the parent when they're ready. Then, the parent knows the child has the urge-elimination association, and uses it to train them.
Some parents are so perceptive, they can tell when a baby is about to pee. They'll whip off the diaper, rush to the potty/sink/whatever and make a sound/use specific words (e.g. "go potty"). The baby urinates. Done consistently enough with a receptive child, it works. The parent cues the child ("go potty") and the child does so. This method is called "elimination communication". It's a kind of operant conditioning.
Are we maybe doing this completely wrong in general? Do you have any tips or guidelines?
No, you're not. Guidelines aplenty in the sources linked to. My tip: always, always keep it positive. Use praise and, if necessary, bribes to get child to cooperate. My first born was potty trained early (positive reinforcement only). When my second child was born, the first backslid. With the appropriate reward (never punishment), they retrained themselves in two short days. (It was a video they liked. Our first video. The perfect bribe works wonders.) My first grandchild was pretty resistant and was bribed regularly. As long as they sat on the potty, they could watch (select) videos. (Eventually they had to pee, which then was met with great praise!)
Is she not ready yet and we should wait a few months again? Or would that be counterproductive?
You know better than we do; you see your child every day. There is some literature that suggests waiting too long may result in more long-term elimination problems, but most of Western literature advocated starting not before 18 months and by 30 months.
How should we proceed now? It will be very difficult again to convince her to put on panties. Once we manage to do it again, we want to have the right approach.
There is no one right approach. Pick one that looks like it will work with your particular child and try it for a while. If it fails, try something else. If at first you don't succeed, try, try again. I suggest always, undeviatingly keeping it positive. Not every authority agrees with me.
There is a lot of history and toilet training philosophy in the links below. It should convince you that there's no one single approach that is "right". I do, however, advocate the child-centered approach, but unlike the American Academy of Pediatrics, I disagree with the subtle use of peer-pressure to encourage success in achieving full continence. I prefer the perfect bribe, and found one for each child.
Some parents who favor authoritarian-style parenting would disagree with any bribes at all. I kind of see a paycheck as a bribe of a sort. Who happily works for free only because someone tells them to?
Toilet Training
Toilet Training: Common Questions and Answers
The American Family Physician handout on toilet training, 2019
