Use the Battlelogium wrapper (community-made) or just rely on the in-game browser.

Re: Battlelog Web Plugin Issues or installation | EA Forums - 6353843

You can often find the old plugin files in installation directories or archived installers.

Battlelog web plugins were more than just a piece of middleware; they were an ambitious attempt to make gaming a truly persistent, multi-screen experience. Though the official plugins are now largely deprecated in favor of integrated menus, the spirit of Battlelog lives on through community archives and the continued use of BBLog by those still fighting on the digital fronts of Battlefield 4 . It stands as a reminder of a time when the boundary between the game and the internet was proudly blurred. AI responses may include mistakes. Learn more

There were generally two components involved:

EA/DICE eventually abandoned the system entirely in 2020, forcing players into the inferior Battlefield 4 in-game server browser (which lacked many battlelog features). The plugins were a classic case of "clever web tech" that aged like milk.

If you are interested in reverse engineering or understanding how this worked, here is the technical breakdown:

Managing social features like chat and party invites through the browser sidebar. The Shift to "Plugin-Free" Launching