If you're careful you can do them in either order.
However for what it's worth here's how the professional workflow on a jobsite interior is set up
rough carpenters
plumbers
electricians
drywallers
finish carpenters
ceiling hangers
painters
floor covering (carpet, tile, etc)
Paint first. There is no use in cleaning a carpet that might get paint on it later. Paint first just in case you end up getting the carpet dirty so you don't have to clean twice.
almond DULUX paint
There should be no need to steam clean fresh paint. If steam cleaning near fresh paint, one should give the paint a few days. Paint and concrete may seem "dry" but they need to cure
mineral spirits.
huh?
Paint.
Some parts you should paint as you build it but otherwise you should build it then paint it
On the soft vinyl you should use a vinyl paint and on the hard plastics use a epoxy paint or plastic paint. Make sure to thoroughly clean all surfaces to be painted with acetone or TSP then rinse in clean water.
Rub it with Goof Off for a few minutes and it should soften. If you can peel parts off do it . Persist with the Goof Off if the carpet will stand it.
Painting a house should be bid by the job, not by the hour. You are being paid to paint, not clean up your equipment.
Painter's tape should be removed after the paint "sets up" and before the paint completely cures.
The condition of being something that no one wants- the opposite of envy. "He had the unenviable job of trying to clean up the red paint that spilled on the white carpet."