Conservativity of ultrafilters with the P-point and Ramsey properties

Let $T$ be one of

$$\mathbf{ACA_0},\quad \mathbf{ATR_0},\quad \mathbf{\Pi^1_1\mathchar`-CA_0}.$$

An ultrafilter $\mathfrak{U}$ is a $P$-point if, for every partition $\mathbb{N}=S_0\cup S_1\cup\cdots$ with $S_n\notin\mathfrak{U}$ for every $n$, there is an $A\in\mathfrak{U}$ such that $A\cap S_n$ is finite for every $n$. It is Ramsey if under the same hypothesis there is an $A\in\mathfrak{U}$ such that $|A\cap S_n|=1$ for every $n$. P-point and Ramsey ultrafilter conservativity conjecture. For each such $T$, both

$$T+\text{“$\mathfrak{U}$ is a $P$-point”}$$

and

$$T+\text{“$\mathfrak{U}$ is Ramsey”}$$

are conservative over $T$. These claims concern whether adding ultrafilters with set-theoretic properties whose existence is independent of ZFC produces no new consequences over the listed reverse-mathematical base theories. The source only says that the forcing construction may adapt to these properties and supplies no proof or counterexample.