But those lawsuits were well settled long before Linux saw a significant inflection point, mostly with the rise of cloud computing. For example, AWS launched EC2 in 2006 (and Android 2 years after that), 12 years after the BSD lawsuit was settled. Linux still doesn't have a desktop footprint outside of the workstation market. By contrast, Apple (well, NeXT) incorporated portions of FreeBSD and NetBSD into their operating system.
This might be a controversial opinion but: Linux likely "won" because it was better in the right areas.
Linux was already used heavily long before "cloud" computing became a coined term. Not just for cheap hosting providers either, in the early 00s Linux dominated the 500 super computers. I also remember repairing an enterprise satellite box in 2002 which ran Linux.
You're right that those law suits were settled long before Linux gained momentum though. FreeBSD and NetBSD were released after Linux and their predecessor (386BSD) is very approximately as old as Linux (work started on it long before Linux but it's first release was after Linux). As far as I can recall, 386BSD wasn't targeted by lawsuits.
Also wasn't BSD used heavily by local ISPs in the 90s?
In any case, I think Linux's success was more down to it being a "hacker" OS. People would tinker with it for fun in ways people didn't with BSD. Then those people eventually got decision making jobs and stuck with Linux because that's where their experience was. So if anything, Linux "won" not because it was "better" than BSD on a technical level but likely because it was "worse" which lead to it becoming more of a fun project to play with.
This might be a controversial opinion but: Linux likely "won" because it was better in the right areas.