For anyone who wants to use it on an older Unity version (like 2019.4), you can use external tools like AutoHotKey to provide the sidebutton functionality.
Here’s a working AHK script for that:
#If WinActive("ahk_exe Unity.exe")
;mouse lower side-button
$XButton1::Send, {F13}
;mouse upper side-button
$XButton2::Send, {F14}
#If
You then just need to remove the HistoryWindow.cs and SettingsWindow.cs (cause they contain some logic to newer Unity API and are optional anyway), as well as any references to them. The Persistence.cs and Settings.cs classes also use the FilePathAttribute, which is internal in older Unity versions. You can either copy the decompiled versions of FilePathattribute and ScriptableSingleton in the package or remove the persistence logic if you don’t need it.
Also in the TabTracker.cs you have to replace the GetFocusedProjectTab function with something like:
public static EditorWindow GetFocusedProjectTab() => Reflector.GetAllProjectBrowsers().Cast<EditorWindow>().FirstOrDefault();
as the hasFocus flag in EditorWindow doesn’t exist in older versions. This removes the support for multiple project windows, but most people probably only have one open anyway.
Once there are no more compile errors, you can head to Edit>Shortcuts… in Unity, find the ‘Move Backward’ and ‘Move Forward’ options and double-click on them to assign them new shortcuts, then press the mouse sidebuttons to insert F13 and F14.