> ...run it in some kind of secure container which has access to read browser history, and write to its database, but definitely does not have network access.

We should be doing this with all software, regardless of provenance, anyway. Least privilege applies to servers just as much as it does to users. Even if the software isn't untrustworthy you can be it has vulnerabilities.

My first go-to is network segmentation because I spend most of my time doing networking work. For every vendor who has shit-talked me to Customers ("Wah, wah! Your networking vendor is making this so much harder because they want us to enumerate our traffic!") I have concrete examples I can cite when attacks were stopped by network segmentation (preventing shellcode from downloading a payload, preventing C2 communication, firing off alerts when unexpected network traffic starts coming out of a host, etc).

Beyond network segmentation, I am very suspicious of software that needs to run as a privileged user. So many attacks get easier when privilege escalation in the host OS is already done for you.