What's the latest iOS that iPhone SEs shipped with?
While the iPhone SE originally shipped with iOS 9.3, you'd most likely not find find a recently manufactured one coming pre-installed with iOS 9.3 (or a later version of iOS 9.x).

iPhone SE models was discontinued on March 21, 2017 (16 and 64 GB variants) and September 12, 2018 (32 and 128 GB variants). Either one of these models, which you'd most likely find with a reseller who is still selling them, would most likely come pre-installed with either iOS 10 or later (but still below iOS 13).

If iOS 9.x is what you are looking for to access iOS 9 exclusive apps, here's the list of iOS devices that can't be upgraded past iOS 9.x. Getting access to one of them could serve your purpose:


iPhone 4S (latest operating system: iOS 9.3.6).
iPod Touch 5th generation (latest operating system: iOS 9.3.5).
iPad 2 (latest operating system: iOS 9.3.6 (Wi-Fi + cellular (CDMA)), iOS 9.3.5 (Wi-Fi and Wi-Fi + cellular (GSM))).
iPad 3rd generation (latest operating system: iOS 9.3.6 (Wi-Fi + cellular), iOS 9.3.5 (Wi-Fi).
iPad mini (latest operating system: iOS 9.3.6 (Wi-Fi + cellular), iOS 9.3.5 (Wi-Fi).


Source: List of iOS devices