It appears that installing of old apps is banned on Android 14. This includes trying to install them from other places than PlayStore.
The biggest news is that Android 14 will block the installation of old Android apps. As Android changes over the years, new APIs and increased security, privacy, or background processing restrictions could break old apps, but Android's backward-compatibility system keeps these old apps running. Apps can declare the newest version of Android they support via a "Target SDK" flag.
To prevent old apps from breaking, new features and app restrictions in, say, Android 12 only apply to apps that target Android 12 or above. Older apps will continue to run with the older set of restrictions they're used to. (A different setting, called "Minimum SDK," determines if a new app can run on an old Android OS.) The system works great for honest developers, but if you're building a piece of malware, it's an easy decision to target a very old version of Android. While you'll get access to fewer features, you'll also be subject to fewer security and privacy restrictions.
From Android 14 Preview 1 is out, will officially ban installation of old apps
A change coming with Android 14 will impose restrictions on the apps that smartphone users can install on their devices, even if they’re sideloading software rather than installing it through the Play Store.
Google’s change should help stop the spread of malware that takes advantage of exploits found in older builds of its Android OS, though if you’re a frequent sideloader it may make it a little harder to use non-Play Store apps.
From Android 14 could stop you from installing older apps – and that’s a good thing
The requirement for targetSDK >=23 is embedded in the Android Compatibility Definition Document for Android 14 CDD, Section 3.1 Software - Managed API Compatibility
[C-0-8] MUST NOT support installing applications targeting an API level less than 23.
So for devices released with Android 14 and Google Play Services, old apps (free and paid) cannot be installed even if side-loaded. Custom ROM developers may ignore such rule but as the Android Open Source Project (AOSP) advances the removal of legacy APIs will make such old apps crash unless the custom ROM developer backports support which does require effort on the part of the custom ROM developer.