How do you get a feel for new characters?

I don’t write out a whole thing for it, but I always came up with relatively full backstories for the characters. If I actually wrote it down on paper the backstories would maybe be a page long or two at the very most.

I do what I do when I people watch. Imagine the persons life through moments to get to where they are now and how they must be feeling about being in this moment.

I suppose it helps that I create characters with specific motivations in mind. This character serves to examine this or that. I’ll give two examples:

I wrote a story once about a 50 year old divorcee, she was a professor and would begin an affair with a former student of hers. I created that character because I wanted to explore the idea of someone regretting being a mother, being a wife, and essentially just regretting the biggest parts of her life.

For another story I came up with two characters. Both in their 30s, they were both interested in music but one was more active in pursuing that than the other when they were adolescent. Cut to today, and the one that was more active on that front never became the pop star they wanted to be, and the other one sort of fell into success. And I created the unsuccessful character to reflect my own experiences of inadequacies and being a loser and not living the life I expected. And the successful character was to explore the actual drawbacks of success, or what I imagine them to be and how not everyone’s cut out for that.

So because I come at character from that perspective it’s a little bit easier to fill them in.

I'm a minimalist at heart, and my characters are a function of the story I wanna tell. They often emerge from the story, not the other way around. I will only describe what is relevant to the story, so you won't necessarily know how they look. They don't even have a name sometimes. In some of my old stories, I made it intentionally difficult for the reader to know who was even speaking sometimes.

I have a hard time understanding why I should flesh out my characters in great detail before writing a story, and when I do, I rarely feel like that was a good way to spend my time. I fully acknowledge that most people probably shouldn't write the way I do. Lots of general writing advice doesn't apply to minimalism, minimal-like styles, as well as some examples of magical realism, comedy, absurdism, hard sci-fi, etc.

Or, generally speaking, stories where concepts and ideas are more important than characters.

Perhaps my answer to How do you get a feel for new characters? is that I really don't. I get a feel for the story, and characters emerge from that.

I find that I can only develop characters in pairs or groups. Which I guess makes sense, since conflict is what interests me. When I'm writing, I always start with a theme I want to explore, and so I sort of imagine characters initially and in subsequent development as representative of conflicting perspectives on that theme. From there, you can work backwards and forwards to flesh them out: backwards by imagining what kind of life experiences and traumas led to their developing that perspective; forwards by determining how that perspective shapes their behavior and personality. But the result of this process is basically just a set of conflict units; colorless, shapeless, unpersonable blobs.
When it comes to making the characters likeable and engaging, I start by trying to build out their dialogue voice. I do this by taking a couple characters and writing a dialogue scene for them, in script format, that has not much to do with the plot or theme of the actual story. In the process of writing a scene about, I don't know, scheduling a trip to the opera, I find that a unique voice, a rhythm and dynamic, emerges out of my subconscious. And from understanding how characters speak and interact, it's easy to flesh out a more complete and colorful personality. I think the shape and structure of dialogue -- not even its contents! can be the most efficient way to characterize someone, and that works in both directions, for the reader understanding the characters and the writer spinning them up, though if you don't already agree with me I can't convince you of it, since it's very primal.
Once I have distinct and natural voices for the characters, I just start writing the work itself, aggressively and periodically rewriting the opening few pages/chapters/whatever. The necessities of exposition will force you to flesh out anything that's missing from the characters, add whatever color and volume is needed, so no point in overthinking it.

I kinda write with the beginning and end in mind so I don't get stuck with a plot that I don't know how to end, so that allows me to pretend I'm doing a 4th wall interview with them about the events of the plot kinda like John Wheeler's reverse 20 questions game where the yes/no answers are random and the topic is retroactively derived from them.

This leads to a lot of meta surprises! Often times things that seem like inconsistencies can be recontextualized - subtle nuances in what a character means, limits in their perspective, actually just a different timeline - so questioning anything that looks like a plot hole often leads to a lot more depth!

I like to mind map characters on a timeline in an infinite canvas like draw.io.
Will put the character in the middle where everything left is Backstory, everything right is Plot.
Start with genre and the tropes I'd like to borrow from. Then figure out arcs and I find the plot most likely inverts the backstory. Tragic Backstory, Triumphant Plot or vice versa. And its a matter of figuring out whats the internal journey they need to go on to achieve some external goal.

Then it's the hard part of differentiating character and identity. Making it clear that they are the same person with developments to their behaviour and mindset. My template is to have some things set in stone from Backstory and make big changes a constant "word-in-progress" or a fight against regression. The further back or deeper down some character trait goes, the more effort is needed to overcome it. But some progress is needed to resolve the central conflict.

From there its just jumping between a lot of different ideas and linking them to points the arc, themes and each other. Apearance, setting, scenes, diction, quirks, habits, other characters. I tend to end up with what looks like an all out conspiracy board tracking multiple parties and everything they ever done.

This style helps me keep things on track as I plot but also allows me to throw in details or elements as I discover them. However it can become a procrastination trap where I go well beyond the scope into irrelevant territory.

I am trying to move this system into an Obsidian Canvas to help keep track of things since referencing details or relationships gets tedious with larger scales.

Probably not exactly what you're looking for, but I'm an actor at heart and I find the best way to discover a character is to live in their shoes a bit. Most of my "theatrical" work in recent years has been roleplaying in D&D and other tabletop games.

Usually I do very little to flesh out my character before I start playing them. At most, I come up with a cornerstone phrase that helps me tune into the character's mindset and dialect, and have a general idea of where they come from and what they want. Then I let them loose in the world and let them surprise me.

My most recent character was my most fleshed out though, I actually wrote up a short introduction with the proposed backstory for my character as we were about to run through the Dungeon of the Mad Mage and I wanted someone with a real direction if we were actually going to play through to level 20 (we didn't, surprise surprise). Even so, she still grew as we played and I developed a better understanding of her as a person. Now she lives rent-free in my head along with the rest of my past characters.