Pointless giving job titles with zero context, we have no way of knowing whether these are full time permanent jobs or part time and/or temp, or why the role may be needed or wanted, or whether that's one aspect of a job that covers many duties.
Walking co-ordinator - doubt this is a full time role, I've seen many "jobs" advertised for local government which are part time, irregular (e.g. 2 evenings a month minuting meetings, then 4 hours per month writing up & distributing minutes & agendas), or even volunteer "jobs".
Roller disco coach: Without context, and whether this was a one off event, impossible to tell.
Bouncy castle attendant: See above. Or possibly a council run soft play type venue, where this type of role is absolutely critical!
Equality and Diversity Advisors: Absolutely critical part of HR! You still get sexism, racism, ageism, and disablism in offices. They ensure that reasonable adjustments can be made for staff with disabilities so they can work without discomfort etc. They ensure that people aren't disadvantaged or bullied because of any differences they may have, or disadvantaged because they have children. Or called racist slurs.
Sustainability officers: These roles usually ARE "integrated into other departments", they won't be an entire directorate of their own. Usually under something like communities, environment etc.
Transformation teams: Yep these teams tend to be put together for specific projects, and as that project winds down the permanent staff are then redeployed onto the next project, then the next. Of course a project isn't just implemented and that's it anyway; there is usually reviews after 3, 6 and 12 months at least (depending on the type of project) to tweak things, ensure they've been implemented properly, ensure that you're getting the results you envisioned, see if more needs to be done in an area. So someone could well have moved on mostly to a new project, but still be "recalled" to perform reviews, or there may be staff who's main role is post implementation work. And of course some of the jobs advertised for this type of work are on fixed term or rolling contracts until the end of a project.