S&S ISA safe savings limit?

I’m aware of the £85,000 savings limit per institution butis there is a similar limit for S&S ISA’s in case the provider were to fail?

The investment protections scheme exists. However, given the way investments are structured, the benefit of the FSCS on unit linked holdings is not that much of benefit. You are not likely to be invested in the S&S provider. You are likely to be invested in funds which are ringfenced and held under an arrangement where the funds cannot be used by the provider.

Would it make sense to move some of the ISA to a differentprovider or transfer it into a cash ISA?

It is unlikely an S&S ISA from the old CIS is going to be good value or best option. However, the FSCS protection is not a reason to change your risk profile and resulting outcomes.