Finally: The newest Govee floor lamp model (what I call a “spike lamp“ although I don’t know if anybody else does) supports Matter over WiFi, so it should work out of the box with SmartThings:
https://www.amazon.com/Govee-Matter-1725lm-Control-Bedroom/dp/B0CTH2QF23
UK link:
https://www.amazon.co.uk/Govee-Matter-Corner-Control-Bedroom/dp/B0CWGN558V/
This is a different, newer model than the one you previously linked to. 
Shane Whatley, Who does excellent HomeKit and matter videos, has an in-depth unboxing review with all the details. Note that the lamp does come with a button remote as well. You’ll only be able to use that to control the lamp, not anything else, but it’s still a nice option to have.
As always, some of the fanciest features will only be available through the Govee app, but of course the great thing about matter is that you have access to the device from multiple platforms at the same time.
On the day of this posting, there’s even a discount coupon on the Amazon page.
(Also be aware that Govee also just released a new “pro version“ that has an included speaker, but does not have matter support, so that one will not work with SmartThings. Shane covers both the new models in his video.)
So this looks like what you were hoping for, although I don’t know if the cost fits your budget. 
