In a braided monoidal category $(\mathcal{C},\otimes_{\mathcal{C}},\mathbf{1}_{\mathcal{C}},\alpha,\lambda,\rho,\beta)$, we have $\beta_{\mathbf{1}_{\mathcal{C}},\mathbf{1}_{\mathcal{C}}}=\mathrm{id}_{\mathbf{1}_{\mathcal{C}}\otimes_{\mathcal{C}}\mathbf{1}_{\mathcal{C}}}$ and the diagrams

commute.

In a braided monoidal bicategory $(\mathcal{C}$, $\otimes_{\mathcal{C}}$, $\mathbf{1}_{\mathcal{C}}$, $(\alpha,\alpha^{\bullet},\phi,\phi^{\bullet})$, $(\lambda,\lambda^{\bullet},\eta,\eta^{\bullet})$, $(\rho,\rho^{\bullet},\epsilon,\epsilon^{\bullet})$, $\pi\mspace{-9.5mu}\pi$, $\mu\mspace{-10.0mu}\mu$, $\lambda\mspace{-10.0mu}\lambda$, $\rho\mspace{-10.0mu}\rho$, $(\beta,\beta^{\bullet},\gamma,\gamma^{\bullet})$, $R_{-,-|-}$, $R_{-|-,-})$, these identities should be replaced by invertible $2$-cells $$ \begin{align*} \mathrm{id}_{\mathbf{1}_{\mathcal{C}}\otimes_{\mathcal{C}}\mathbf{1}_{\mathcal{C}}} &\Longrightarrow \beta_{\mathbf{1}_{\mathcal{C}},\mathbf{1}_{\mathcal{C}}}\\ \lambda_{A} &\Longrightarrow \rho_{A}\circ\beta_{\mathbf{1}_{\mathcal{C}},A},\\ \rho_{A} &\Longrightarrow \lambda_{A}\circ\beta_{A,\mathbf{1}_{\mathcal{C}}}, \end{align*} $$ similarly to how the identity $\lambda_{\mathbf{1}_{\mathcal{C}}}=\rho_{\mathbf{1}_{\mathcal{C}}}$ in a monoidal category is replaced by an invertible $2$-cell $\theta\colon\lambda_{\mathbf{1}_{\mathcal{C}}}\Longrightarrow\rho_{\mathbf{1}_{\mathcal{C}}}$ in a monoidal bicategory (see [Enriched categories as a free cocompletion, Lemma 2.1]).

Question: How are the above $2$-cells constructed from the data $(\mathcal{C},\ldots,R_{-|,-,-})$?