i would seriously consider sqlite-utils here.
MySQL or Postgres with their native JSON datatypes _might_ be faster, but you still have to load it in, and storing/indexing it in either of those is [0] its own [1] special nightmare full of footguns.
Having done similar text manipulation and searches with giant CSV files, parallel and xsv [2] is the way to go.
[0]: https://dev.mysql.com/doc/refman/8.0/en/json.html
[1]: https://www.postgresql.org/docs/current/datatype-json.html
It doesn't handle streaming JSON out of the box though, so you'd need to write some custom code on top of something like ijson to avoid loading the entire JSON file into memory first.
In my personal experience I’m usually digging through structured logs to answer one or two questions, after which point I won’t need the exact same data set to be indexed the exact same way again. That’s often more easily done by converting the data to TSV and using awk and other command line tools, which is typically quicker and more parallelizable than loading the whole works into SQLite and doing the work there.