I spend a lot of time around people who are kayaking coaches so safety and training comes up (far too much) in general conversation. I get bored to death on this subject on a regular basis! But I also really appreciate how seriously these issues are taken by so many coaches.
You should ALWAYS have a safety briefing (even if you have done it before) and equipment should always be checked that it fits appropriately. Refusal to use equipment should be an automatic 'you are not doing it'.
If you are nervous, tell the instructor before. They should take that into account and have a chat with you about it. Its recognised that men and women often have different levels of anxiety over doing these sports - in part because women know they have less power and strength. Good coaches are taught to identify different ways to approach this. They should take things at a pace everyone is happy with and if you don't want to do something it's encouraged to say so.
The BCU is really strict in its expectations and training. If a coach is on a beach playing with their kid building sandcastles and sees someone doing something daft (eg going out on an inflatable without a buoyancy aid) they have an obligation to go and have a word and warn rather than just ignore it. They also have an obligation to go help if they see someone in trouble. If they don't they could lose their accreditation even though they aren't taking a session and don't have direct responsibility if they are present when an incident happens .
There's been several incidents where DH has rescued dickheads and got abuse for telling someone the dangers. He's not alone. I hear lots of stories about idiots attempting a Darwin Award. I dislike going certain places if it's 'silly season' because DH is always looking out for numpties. It worries me because it put him and good friends potentially at risk.
I also know that the BCU has supported women only sessions and understanding differences in confidence/ bravado that stem from this and promoting awareness of this amongst coaches. This is fab and I really appreciate it. Some are better at this than others but it's definitely recognised by many.
I would add that paddleboarding has had a particularly bad reputation on being slack on understanding safety before this incident for some time. I know a lot of kayakers were talking about how it would take 'another Lyme Bay accident' https://en.m.wikipedia.org/wiki/Lyme_Bay_canoeing_disaster for it to change.
Sadly here we are. It was totally predictable and was expected by many who were powerless to do anything. There were too many idiots who were 'too cool' to be seen in a buoyancy aid who gave lip to people who were regularly seeing health and safety disasters waiting to happen as it had been taught as part of their training what happened. Paddleboarding had a very different culture and attitude which was much more macho and image based. Unfortunately kayakers weren't taken seriously in their concerns until it's been too late. Paddleboarding culture is being forced to change to take this much more seriously but it's going to take time and unfortunately since paddleboards are relatively cheap you still see teens in North Wales with no buoyancy aid and no one looking after them far too often. If you don't have experience and training do not go out without a guide - particularly at the coast. It is that simple. If someone tells you, you are doing something unwise, listen to them - it might save your life.
As I say since this accident the BCU has taken control over regulation and safety training for paddleboarding because it was recognised that the organisation have identified that the BCU has the experience, knowledge and culture to help. Hopefully it will help to stop so many incidents.
Accidents do still occasionally sadly happen - it's inevitable - but when they do, most come back with the same classic failings. It's awful especially because they are usually so foreseeable and thus preventable.
If in doubt ask about qualifications. If you see something you don't like, challenge it or talk to the BCU about it. The one I would keep most of an eye on is the ratio of coaches to clients. The culture of the body is to identify problems and it does have a strong H&S ethos which supports reporting and questioning.
In the UK kayaking/canoeing is generally safe as a result. (I'm still wary of paddleboarding for now - give it a few more years). The BCU standards are held as gold standard and usually other countries recognise BCU accreditation (this is one reason why you get a lot of British coaches elsewhere in the world too). Unfortunately it's not as strictly regulated everywhere and actually you should probably be more wary doing watersports whilst on holiday abroad as regulations aren't the same and it's perhaps more tempting in the sun and warmer water...