because I believe that in the future, the governments will make it very difficult to share copyrighted media online
How do you believe this will happen? I hear this sentiment a lot but never a well put together explanation of how one thinks this is possible...
over 200,000 bookmarks
You're a mad mad, I love it. In answer to your question yes probably, most browsers aren't storing your bookmarks in ram at all times and even a 10 million line txt file isn't so large so you could get away with it if they did. The only lag you're going to see will be very slight when you first load the browser, if you're running a half decent ssd this wont be a problem at all.
I say this without knowing if there is browsers that hardcoded a limit for how many you can have but I doubt they did, not expecting people to have as many as you never mind millions.
You mention privacy in not uploading/syncing your bookmark but assuming you're not doing anything illegal and the majority aren't behind login/paywalls then that list of urls is valuable to projects like ArchiveTeams URLs effort for wayback ingest.
archive.org hands down, wouldn't consider anywhere else for this material.