Ah but I'd want to run it myself anyway. I wouldn't want it hosted. Especially for browsing, I don't want someone else's systems looking over my shoulder.
I avoid cloud stuff as much as possible in my personal life. When you mentioned github actions I thought it was something you could self-host too, I didn't realise it was a service only. I was looking for a docker or something but as it's not free and (less importantly) foss it won't work for me.
And yes neko is not a polished corporate solution, but it works for me as a home user. It's very flexible to build other stuff with. I have several instances here in different environments (and I don't expose them to the clear internet)
But for work yeah I know there's different options, at work we have zscaler remote browser.
As to cloud - indeed, why would you want to trust a cloud provider with sensitive internal browsing? Also, providing a SaaS is a hassle, but I feel I must do it serve that side and enable those uses, some of which are cool.