What works for some may not work for others but this is what I do. Hope it sparks some ideas for you:
On short races –
– Bottle in a cage + mini pump next to it.
– Spare tube, levers, small multitool with a chainbreaker, spare link and patches in an Ortileb saddle pack (doesn’t foul dropper posts)
– bars, gels, phone, car keys etc. stashed in short or jersey pockets (SWAT stuff is pretty good or just regular “roadie” jerseys)
On longer races I add a small bladder back pack and stuff a banana and a few extras in with the water.
If it looks like rain, I’ve got a small stuff pack waterproof that nicely straps into the corner between the top and seat tube.
I figure in a race situation, there isn’t much point in carrying first aid. If pushed, you can improvise with other kit but there are usually marshals and others around who can help a lot more than a sling, a bandage and a few plasters.