So, you want to know about Stellaris multiplayer? Like all of Paradox's iconic grand strategy games, even though Stellaris is primarily geared towards solo play versus AI opponents, everything can be done in multiplayer as well. Up to 32 players can compete for dominance over the galaxy, although smaller groups can always work together in co-op as well to take on the other AI-driven empires.
Multiplayer in Paradox strategy games has always been a bit of an inconsistent aspect of the game - the backend infrastructure has historically been a bit weak, desyncs can happen frequently, especially with high player counts, and overall online players only make up a small percentage of any one game's player base (it will vary from game to game).
As of August 2021, Stellaris uses the Nakama infrastructure to power its multiplayer backend. This was developed by the third party, and completely replaces Paradox's previous internal infrastructure, and most notably enables cross-platform multiplayer between stores. The developers believe this version will be way more stable than their previous version, and it's also been rolled out to other older games such as EU4.
RELATED LINKS:
Stellaris Enigmatic Fortress - a quick guide
The best Stellaris mods
Stellaris dev diary - all the latest information