It's hard to tell the scale from your photo, but that looks like a small gap that can be easily caulked. Quality caulk should not sink if it's done properly. But you can caulk it, and then re-caulk the next day if you don't like the appearance. Then prime and paint.

Obviously, choose a caulk that says it is paintable.

My *favorite* caulk for stuff like this is "ALEX PLUS 10.1 oz. Clear Acrylic Latex Caulk Plus Silicone" It is NOT 100% silicone; it is paintable, siliconized caulk that dries clear. I have found that over time (10+ years at this point) the places I used this caulk remain well-painted and clean. The places where I used a white caulk have yellowed, even underneath the paint. The clear is also a bit more flexible than your basic 'painters caulk' so it doesn't crack. I apply it in the crack, and smooth with a damp finger.

Can't help on the order of operations if you are priming trim, I only ever painted over the existing (not perfect there)

@kats737 thank you for bringing up yellowing. i painted over caulk at our bathroom vanity, think it was clear, and it still looks good 8 years later.