I have a MIDI keyboard linked to my laptop with Reaper software. There, I can access all of my VST collection. The question is: what kind of keyboard must I have to play live and get my VST list on it?
The usual setup is a laptop plus keyboard with MIDI.
I've never heard of a keyboard that runs VST instruments natively, but there were some external rack units and pedals (for guitar players) that either existed or were announced. I don't think any of them really caught on, though. The problem is that it basically needs to be a computer itself. But they need to design it themselves to fit in a little box, stay cool, and be at least as reliable as a laptop. This inevitably results in it being more expensive than a laptop and with a worse interface (small screen, no trackpad). In other words the concept was pretty much destined to fail.
So you already have the cheapest and most usable setup. If it were me I'd probably want some kind of stage keyboard that also has a MIDI out so that in case your computer dies in the middle the of gig you could switch to the onboard sounds. Also in terms of reliability maybe have a laptop dedicated to stage/studio use that only gets updated periodically and won't get bricked by normal day-to-day usage. That can get expensive though.
It doesn't appear that there are any keyboards that will let you directly load VSTs into them. The most common way to use VSTs live is to simply use a laptop with a small USB audio interface that you can plug into the soundboard.
EDIT: it appears the standalone hardware VST host company SM Pro Audio is out of business. Even though you can still get them on Amazon. It's probably best not to.