Scheimbauer’s factorization-algebra comparison conjecture

Let $\mathcal{C}$ be a nice $\use@mathgroup \M@U \symAMSb{E}_{n}$-monoidal $\infty$-category. Let $\mathfrak{Alg}_{n}^{\textup{FA}}(\mathcal{C})$ denote Scheimbauer’s $(\infty,n+1)$-category of $\use@mathgroup \M@U \symAMSb{E}_{n}$-algebras in $\mathcal{C}$ defined using factorization algebras, and let $\mathcal{C}_{I/}$ be the relevant pointed slice category. Factorization-algebra comparison conjecture. There is an equivalence

$$\mathfrak{Alg}_{n}^{\textup{FA}}(\mathcal{C})\simeq\mathfrak{Alg}_{n}(\mathcal{C}_{I/}).$$

This comparison would identify Scheimbauer’s pointed bimodule construction with the unpointed construction studied in the paper. The source presents it as an expectation for nice $\use@mathgroup \M@U \symAMSb{E}_{n}$-monoidal infinity-categories and gives no resolution.