Photoshop CS6 or Photoshop CS6 Extended

Back in the bad old days of Creative Suite, there was a plain Jane basic version of Photoshop and an Extended version of Photoshop.  Those days are gone.  Nowadays, we have one Photoshop CC which contains all the bells & whistles of Creative Suite extended and more...

MODERN OPTIONS:
Photoshop Elements is a light version without all the bells & whistles (approx $100, no subscription needed).
https://www.adobe.com/products/photoshop-elements.html

Creative Cloud Photography Plan (approx $10/month for 12 months). Includes the following:
- Photoshop CC and Photoshop on iPad
- Lightroom on desktop, mobile and the web
- Lightroom Classic
- Portfolio website + hosting
- Spark with premium features
- Bridge

- Various mobile apps
- 20 GB cloud storage (upgradable to 1 TB).
https://www.adobe.com/creativecloud/photography.html

Creative Cloud All Apps (51 + apps & services) and Single App Plans
https://www.adobe.com/creativecloud/plans.html

Do I have my facts wrong?

Your facts are correct for CS6 but CS6 was superseded years ago. The distinction between Standard and Extended disappeared when the Adobe Cloud arrived 10 years ago.

You can see how much Photoshop has changed since CS6 here (refer Version History)

https://en.wikipedia.org/wiki/Adobe_Photoshop

The current version of Photoshop you get in the Cloud is far more advanced than CS6 and 3D has always been included with the Cloud version, provided your computer hardware can handle it.

Check system requirements here: https://helpx.adobe.com/photoshop/system-requirements.html

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If I subscribe to the 25$/month Photoshop plan,

If you only want Photoshop then consider subscribing to the $10 (depending on where you live) Cloud Photography Plan rather than the Single App plan (which is the $25 plan you've been looking at). It's a bargain price and you get Lightroom as well. You don't have to use Lightroom if you don't use it but you still pay far less than the Single App plan.

There are a couple of different options so compare them here

https://www.adobe.com/creativecloud/photography/compare-plans.html

You do not get CS6 at all, you get the new Cloud subscription version of Photoshop

Cloud Plans https://creative.adobe.com/plans

Special Photography Plan includes Photoshop & Lightroom & Bridge & Mobile Lightroom
The special photography plan is also somewhat like a 'loss leader' advertisement to get you into a grocery store to buy the items on sale, while hoping that you will decide to add other purchases... the photoshop in the special plan is exactly the same as the photoshop sold as a single product for a higher price