add a category to workout on iPhone

According to this article, the default Yoga workout can be used for all kind of Yoga types:

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copied from: Workout types on Apple Watch - Apple Support

Or look for a 3rd party workout app which might support this Yoga style.

You can also add an "Other" workout. Take a look here:

Workout types on Apple Watch - Apple Support

There are also apps for chair yoga in the App Store that you could look into.

Regards.