ci(flatpak): sync with flathub (#3259)

docs/getting_started.md

@@ -53,22 +53,24 @@ CUDA is used for NVFBC capture.
         <td>sunshine-ubuntu-24.04-{arch}.deb</td>
     </tr>
     <tr>
-        <td rowspan="2">12.0.0</td>
-        <td rowspan="4">525.60.13</td>
+        <td rowspan="1">12.0.0</td>
+        <td rowspan="3">525.60.13</td>
         <td rowspan="4">50;52;60;61;62;70;72;75;80;86;87;89;90</td>
-        <td>sunshine_{arch}.flatpak</td>
-    </tr>
-    <tr>
         <td>sunshine-debian-bookworm-{arch}.deb</td>
     </tr>
     <tr>
-        <td>12.4.0</td>
+        <td rowspan="1">12.4.0</td>
         <td>sunshine-fedora-39-{arch}.rpm</td>
     </tr>
     <tr>
-        <td>12.5.1</td>
+        <td rowspan="1">12.5.1</td>
         <td>sunshine.pkg.tar.zst</td>
     </tr>
+    <tr>
+        <td rowspan="1">12.6.2</td>
+        <td rowspan="1">560.35.03</td>
+        <td>sunshine_{arch}.flatpak</td>
+    </tr>
     <tr>
         <td>n/a</td>
         <td>n/a</td>
@@ -188,21 +190,30 @@ sudo dnf remove sunshine
 #### Flatpak
 @caution{Use distro-specific packages instead of the Flatpak if they are available.}
 
-@important{The instructions provided here are for the version supplied in the [latest release][latest-release],
-which does not necessarily match the version in the Flathub repository!}
-
 Using this package requires that you have [Flatpak](https://flatpak.org/setup) installed.
 
-##### Download
+##### Download (local option)
 1. Download `sunshine_{arch}.flatpak` and run the following command.
    @note{Replace `{arch}` with your system architecture.}
 
-##### Install (system level) 
+##### Install (system level)
+**Flathub**
+```bash
+flatpak install --system flathub dev.lizardbyte.app.Sunshine
+```
+
+**Local**
 ```bash
 flatpak install --system ./sunshine_{arch}.flatpak
 ```
 
 ##### Install (user level)
+**Flathub**
+```bash
+flatpak install --user flathub dev.lizardbyte.app.Sunshine
+```
+
+**Local**
 ```bash
 flatpak install --user ./sunshine_{arch}.flatpak
 ```