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This is a calculation using the local cohomology sequence for etale cohomology together with Gabber's relatively recent proof of the absolute purity conjecture. Let $% Y=\operatorname{Spec}(R)$, $X=\operatorname{Spec}( R[t]) $, and let $\sigma \subseteq X$ be the image of a section so that $U=\operatorname{Spec}\left( R[t,t^{-1}]\right) $ is its complement. Gabber's recent proof of absolute purity establishes Grothendieck's purity conjecture for the Brauer group which states that $% H_{\sigma }^{3}\left( X,\mathbb{G}_{m}\right) =H^{1}\left( \sigma ,\mathbb{Q}/\mathbb{% Z}\right) $ if $\sigma \subseteq X$ is a regular subscheme of a regular scheme. Moreover $R\rightarrow R[t,t^{-1}]$ has a section. Thus we have an exact sequence coming from the local cohomology of $\mathbb{G}_{m},$ \begin{equation*} 0\rightarrow Br\left( R\right) \rightarrow Br\left( R[t,t^{-1}]\right) \rightarrow H^{1}\left( R,\mathbb{Q}/\mathbb{Z}\right) \rightarrow 0 \end{equation*} since $H^{3}\left( R,\mathbb{G}_{m}\right) =H^{3}\left( R[t],\mathbb{G}_{m}\right) \hookrightarrow H^{3}(R[t,t^{-1}],\mathbb{G}_{m}).$ Note though that this uses Kummer sequences and homotopy invariance for $\mu_n$ and so only applies to torsion in $Br(R[t,t^{-1}])$ of order invertible in $R.$ In fact you can argue directly with $n$ torsion using Kummer sequences and purity for $\mu_n$ cohomology to get this result for $n$ torsion elements if $n$ is a unit in $R$.
Of course if you puncture the line in more than one point, you get multiple copies of $ H^{1}\left( R,\mathbb{Q}/\mathbb{Z}\right)$.
The easiest way to address $n$ torsion when $n$ is not a unit in $R$ is, I think, to look at the split exact sequence on $R_{et}$ $$ 0\rightarrow k_*\mathbb{G}_{m,R[t]} \rightarrow p_*\mathbb{G}_{m,R[t,t^{-1}]} \rightarrow \mathbb{Z} \rightarrow 0 $$ where the last map is the degree map. The Leray spectral sequence for $k$ and $p$ yield a split exact sequence $$ 0\rightarrow Br(R) \rightarrow Br_{sp}(R[t,t^{-1}]) \rightarrow H^1(R,\mathbb{Q}/\mathbb{Z})\rightarrow 0 $$ where $Br_{sp}(R[t,t^{-1}])$ consists of elenents in $Br(R[t,t^{-1}])$ that are split by passing to $R_{\mathfrak{p}}^{sh}[t,t^{-1}]$ as $R_{\mathfrak{p}}^{sh}$ runs through all strict henselizations of $R$ at prime ideals $\mathfrak{p}$.
Thanks to @CarlWoll:
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It appears that your scan worked correctly through the TOR network. Based on the switches you used, nmap only sent a SYN to port 80 and your target responded with a RST. The timeout from proxychains just means a SYN/ACK wasn't received from the target.