My process is essentially the same, regardless of whether the RPG uses classes or is classless.
I contemplate what the GM has told me about the campaign. Then I try to figure out what kinds of adventures might be had in such a world, and what kind of protagonists might be fun to play in such a setting.
At that point, one of the following happens:
1) I design a brand-new character for the campaign
2) I choose a character that I’ve designed in the past that would work in that campaign, and model it within the relevant RPG & campaign mechanics.
3) I combine 1 & 2
4) as above, but I design or choose a character that fits in the narrower constraints of filling a void that the party still has to fill.
All that said, I’m not necessarily just designing a PC to fit a jigsaw puzzle piece within the party. I’m always looking to design a PC that I will find fun to play in the here & now. Even in the case of a situation noted in 4 (above), I’m going to choose to do so in a way that won’t bore me.
Sometimes, that means leaning into a stereotype; sometimes it’s something most players haven’t seen before.
And the inspirations can come from anywhere: music, art, written fiction, historical reenactments, a single unusual weapon or piece of gear, etc.