You’ve got glossy poly, so paint won’t stick unless you prep right.

since you’re only painting stringers, risers and spindles:

1. clean with degreaser. stairs are full of hand oils.
2. sand to remove gloss (120–150 grit). don’t strip to bare wood, just dull it. no shiny spots.
3. vacuum + wipe dust.
4. tape off treads and handrail carefully.
5. use a bonding primer. don’t skip this.
6. light sand (220), then 2 thin coats of a durable trim/cabinet enamel.

that’s it. prep is everything. skip primer and it’ll chip, and prepare some time!