Does the FSCS protection limit of £85K mean I have to spread my pension pot across different providers?

I haven't checked all of them, but I'm pretty sure all UK SIPP providers will hold (uninvested) client money in trust, or at least in segregated accounts. Here are some examples:

Hargreaves Lansdown

All client money is held by us on trust and is segregated from our own funds in accordance with the FCA’s client money rules and guidance so that any creditors of Hargreaves Lansdown would have no legal right to it and we cannot use any of this money to cover Hargreaves Lansdown's obligations.

Interactive Investor

Any money (cash) held in your account is treated as ‘client money’ as defined by the FCA. This means your money also has trust status, and is deposited across a range of bank accounts specially designated as holding client money. At no point does your cash enter an ii bank account.

Fidelity

(interestingly doesn't use the phrase "in trust")

Investment firms such as Fidelity are very different from banks because we are required to separate client money and assets from our own resources. We are not permitted to use client money and assets in the course of our own business activities, and your money would be ring-fenced in the unlikely event that we became insolvent.

In general a site-specific search for the term fscs will get you to a provider's 'reassurance' page(s).