Is there a preferred set of tools that can be updated?
I think you need to talk to distro people about this.
If not, would it make sense to develop a set of common kernel tools for
this?
Yes, it would, but please see above in the first place.
In my experience, it seems many folks use tools from their vendors or
custom tools.
This observation matches my own experience.
For the sake of discussion, and from a kernel developer's point of view,
should the tools be part of a separate project? Or should the tools be
part of the kernel tree like perf, etc.? Assuming that this needs to
start from scratch and not extending an existing project.
It can be both in principle, but from the practical standpoint it is
more likely to get all of the people to use the same set of tools if
they are included into the kernel source tree.