When the Program Compatibility Assistant message does appear, the Compatibility tab of the program reports that no settings have been applied (which is also the case if the message doesn't appear), yet in some cases, Steam complains that it shouldn't be run in compatibility mode.
In my case, both Windows and Steam didn't warn that compatibly settings had been applied, which makes this issue even more problematic, especially when they can be applied to either Steam, the Overlay or the Steam Service and only a warning is displayed for Steam.
Before this fix, Steam was opening slowly, freezing frequently and hanging on "Preparing to launch..." for games. In addition, Team Fortress 2 froze for 10 seconds whenever the backpack, class loadout or server browser was opened.
After defragging, scanning for errors and scanning for viruses, the issue was still present. It was only after Windows stated that compatibility settings had been applied to "GameOverlayUI.exe" that the cause was found: In regedit under the compatibility layer keys, several items were listed with Steam, including the Steam client itself, which Windows had failed to mention before.
After removing all entries related to Steam, the client opened and logged in almost instantly. The "Preparing to launch..." window appeared for a much shorter duration before playing games too.
Later, after I bought new PC and installed a fresh copy of Windows, Steam was freezing while opening again. The cause once more was that Windows had applied compatibility settings without warning to SteamService.exe, with no warning from Steam either.
In addition, each time Steam is removed from: HKEY_LOCAL_MACHINE\Software\Microsoft\Windows NT\CurrentVersion\AppCompatFlags\Compatibility Assistant\Store\ and then Steam is opened, the entry is added again, although none of issues listed above reoccur after this single entry is re-added.