What and how much safety kit to carry depends on the conditions, the type of paddle that you’re doing and whether you’re responsible for other people. An advanced water sea leader operating in a remote corner of Scotland in winter is going to carry more kit than a member of a group being led on a day paddle around Cornish beaches in high summer.
I’d suggest the following as a start point:
Food (lunch, snacks) and drink (water bottle and/or thermos flask)
A means of summoning external assistance e.g. VHF, PLB, phone, flares - ideally carry more than one option!
Towline - everyone in the group should have a towline and know how to use it.
Knife - always have a knife on hand in case you need to cut an entangled towline. Also useful for cheese at lunchtime.
Whistle - for attracting attention
Compass - hiking baseplate compasses are ideal
Basic first aid kit - to treat simple bumps and scrapes and including any personal medication
Basic repair kit - ‘Flex Tape’ has become my primary approach to repairing things, as it works so well in the wet. Cable ties are always useful, and it’s good to have tools to tighten the bolts on your boat.
Exposure bag or emergency shelter - for treating hypothermic casualties. Exposure bags come in a variety of designs from the traditional orange plastic bag to modern advanced designs like the ‘Blizzard Bag’ that reflect heat and open out to create air pockets that act as insulation. Emergency shelters are larger, such that you can fit an entire group in - like a tent but without the poles.