Your set up is very like my last Wee. Nicely tweaked for me and can go distance with reasonable cost and not too many fuel stops.
It's good in the twisties and stable off pavement with the correct tires.
What it won't do is give you a twist the wrist thrill. A 1000 strom weighs about 25lb more and will give you a nice rush and likely your farkles will translate.
You lose some fuel mileage and range and some luggage weight capacity ( it's the same as the Wee but the bike weighs more ).
Moving to a different marque is risky.
I initially went to a CBF1000 ( similar to your ST1300 but lighter sport tourer ) - got my thrills, not as comfortable, dismal tank range and costly to operate in Canada. It weighed a bit less than the Wee and the weight was lower which helped my 30" inseam.
But how often did I get to use that power ....and far too many fuel stops.
So I gave up on the thrills, went for mileage and low weight with the CB500x.
Not as much oomph even as the 650 Vstrom but enough to tour all day at 80 mph + and truly delightful near 70 mpg fuel economy with a long range between stops.
Weighs less too ....down 70 lb to 422 and that's a treat. I'm 71 and moving the CB500x around is a treat after the 500+ plus machines.
If you are comfortable on your 650 ...I'd be cautious switching out as you get a lot of pluses and they are very reliable ( stator issues excepted )
I bought one 2010 650 ABS specifically for a trip out west with my son and it served very well. Sold it when I got back and then missed it.
Got a super deal on a high mileage same machine and rode it for 20k km and sold it for the same $2200 I paid for it....
Bought the CBF1000 to get the thrill but the range annoyed me to no end and rarely an opportunity to use the power.
Settled on my first new bike in 50 years.
If you fit the Wee ....I'd sit tight. I wanted something a bit lower and bit lighter and cost effective on fuel.