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How is gender generated among spren?

Example: Kaladin's spren Syl manifests as female. Was she female before bonding with him? Or did she choose to manifest as female because Kaladin is a lonely hormonal young man, and it could make the bond stronger? Or yet, did Kaladin's own mind manifest her as female through their interaction?

In this case of Syl, she's almost certainly always been female.

Since spren are creatures of the Cognitive Realm, their gender is partly determined by human perception. As noted in Oathbringer, the oldest spren tend to have four genders:

“So … some of my spears have been women, then?” he asked.

“Female, at least,” Syl said. “Roughly half, as these things tend to
go.” She flitted up into the air in front of him. “It’s your fault for
personifying us, so no complaining. Of course, some of the old spren
have four genders instead of two.”

“What? Why?”

She poked him in the nose. “Because humans didn’t imagine those ones,
silly.” She zipped out in front of him, changing into a field of mist.
When he raised his hand, the Shardblade appeared.

_Oathbringer

My impression from this is that the gender of a particular spren tends to stay constant over their lifetime. Otherwise the old spren wouldn't tend to have four genders, but would instead have changed to be (mostly) male or female, in accordance with the perception of the dominant intelligent species in Roshar's Physical Realm, humans, who are (mostly) male or female.

Human perception doesn't control the traits of an spren at the individual level, at least for the intelligent spren, although flamespren and other less intelligent spren seem to change physically in response to human observation. For instance, we see spren such as Wyndle, who disagree with their bonded Radiants about their nature. Lift is initially convinced that Wyndle is a Voidbringer, but this doesn't make him act like a Voidbringer. I don't think Kaladin's mind controls how Syl manifests.

Thus, since Syl is currently female...

“It doesn’t feel right,” Kaladin replied, still whispering. “You’re a
woman, not a weapon.”

“Wait … so this is about me being a girl?”

“No,” Kaladin said immediately, then hesitated. “Maybe. It just feels
strange.”

_Oathbringer

...then she's not one of the old spren and has always been female.

As far as physical appearance, when Syl manifests in Shadesmar, her form is similar:

Adolin jumped to his feet, scrambling back. He almost collided with a
young woman with blue-white skin, pale as snow, wearing a filmy dress
that rippled in the wind. Another spren stood beside her, with ashen
brown features that seemed to be made of tight cords, the thickness of
hair. She wore ragged clothing, and her eyes had been scratched out,
like a canvas that someone had taken a knife to.

_Oathbringer

While honorspren can change their appearance in the Physical Realm, being essentially made of cloud, I don't believe they can do so in the Cognitive Realm.