On my classic one, I have a Silca frame pump custom painted to match the bike. It’ll pump a tire but mostly it’s just cool.
Otherwise, a regular CO2 can handle one road tire. I carry it for just that.
I’ve brought the CO2 along with a little mini pump on long gravel and mountain bike rides. On stuff where multiple flats can leave me stranded, I do like the pump. Even if it’s slower and annoying.
Tubeless helps, the sealant dramatically decreases the chance I’ll need to fix a flat. Once settled, a tubeless tire can be reinflated with a hand pump.