Apple - How do I determine the version of Bluetooth my iPhone supports?

You can search for your iPhone's technical specifications page by model name (like "iPhone SE") on the apple support site. However, make sure you know what generation you are interested in, if that's a thing with your model. I searched for "iphone se technical specifications" on both the support site and the main Apple site and one site gave me info on 1st gen SE, the other on 2nd gen SE (both labelled "iPhone SE").

The resulting spec page has info about the Bluetooth version supported, so I suppose it is determined by the hardware and not on the iOS version.

UPDATE: It seems you can find a spec page containing bluetooth information on https://everymac.com by searching for the model number "MP8K2LL/A" as well.

Bluetooth Capabilities

What Bluetooth version do these values map to?

Your Bluetooth chip is actually part of the larger wireless chip inside your phone. It could be integrated with the Broadcom or Qualcomm radios or it could be a separate WiFi and Bluetooth module much like the AirPort cards found in Mac computers.

Those versions "map to" the capabilities of the Bluetooth functionality of that chipset. As far as your OS is concerned (macOS, iOS, iPadOS, etc.) it can only make use of what the chip provides. A manufacturer can choose to not enable NFC pairing for example, even though it's part of the Bluetooth 5 standard. The operating system cannot "upgrade" Bluetooth functionality in the same manner that filling your car with ultra high octane racing gas can suddenly make it a contender for the 24 hours at Sebring.

So, to answer your question....

Is it determined by my hardware (such as iPhone SE)?

Yes, but not just your hardware. It also depends on what features that the Bluetooth hardware is capable of that Apple makes available in their operating system (i.e NFC or Near Field Communications)

How to find the technical specifications

Apple maintains a database of the technical specifications for all of it's products at https://support.apple.com/specs. Every product they make is archived here - I checked for the original iPhone and sure enough, it was available.

The Bluetooth information is usually found under the Cellular and wireless section as shown below:

You can get the model number of your device by going to Settings-General-About and then type into google the model number iPad Bluetooth version and it will display pages that have the information. As an example, I have an iPad Pro with model number MPA42LL/A. I typed the following into Google search box:

iPad MPA42ll/A BlueTooth version    

And I got about 4 sites that told me directly the Bluetooth version. It also gives you the generation and name of the iPad.

If you just type in the model number only into Google, you'll get info on that version of Apple Product.

The Bluetooth depends on the hardware, not the System Software.