What is the easiest way to transfer a photo from the Photos app to non-Apple editing software like Illustrator or Photoshop?

If you want simple just hold down the Option key and drag the thumbnail to the Desktop. That will give you the original file. If you've edited it just dragging the thumbnail to the Desktop without the Option key will give you the edited version.

To edit a photo in a different app that does not offer direct integration with photos (looking at you Adobe suite), select your image and then go to File > Export > Export Unmodified Original. You can then save wherever you would like and edit the photo using whatever program you wish.

I just want to quickly find a photo I know is on my Apple devices, drag it somewhere else and have it appear there.

Have you tried just dragging the picture out of Photos to a folder? You get a copy of the edited picture, full resolution.

Which system version do you have installed on your Mac? In the more recent versions of Photos you can use the command "Image > Edit with ..." to open an image in third-party image editors.

Just a little background reading, on the App sandbox for others coming across this discussion - I understand, you find it very restrictive, but it is one of Apple's most important security features to protect the integrity of your application data. Before the sandbox has been introduced, it has not been safe to use drag and drop between applications at all. For example, sometimes, when I dragged an image from Aperture or Photos to Adobe Photoshop CS, the original image file become modified in the library, not just the edited version. I had to recover the originals from Time Machine. Malicious apps could install malware this way.

Apple Developer Documentation: App Sandbox

The App Sandbox is an access control technology that macOS provides and enforces at the kernel level. The sandbox’s primary function is to contain damage to the system and the user’s data if the user executes a compromised app. While the sandbox doesn’t prevent attacks against your app, it does reduce the harm a successful attack can cause by restricting your app to the minimum set of privileges it requires to function properly.

A sandboxed app must explicitly state its intent to access a restricted resource or protected file location, otherwise the system prohibits any attempts it makes at runtime. Xcode’s App Sandbox capability allows you to state that intent by enabling the privileges that your app requires ...

I wonder if you've ever tried to send a photo from Lightroom (or Lightroom Classic), both made by Adobe, to Illustrator - which is not an image editor. Lightroom Classic/Lightroom and Photos all share one common feature: they're photo managers using parametric editing - so that the only way to get an edited image from them to Illustrator is to export it first. I'm not sure why you complain about Apple, when it's pretty much the same workflow with Adobe's own products.

When it comes to Photoshop - which is a pixel editor - again the same workflow is used. All three have a Edit In command, hardwired within the LR family, but equally available in Photos.

So, I wonder what exactly you're complaining about.

Your problem is that you're expecting a parametric editor to behave like a file manager. Lightroom and Photos are the based on the same idea. So it's not different. I'm not sure why you think they would be. For what you want you should not use Photos at all, instead use Bridge, Graphic Converter, the Finder or something else not based on a database.