There's definitely a community around this, though it's smaller than you'd think. The speedrunning scene is real - people track their times seriously and compete on leaderboards. The main thing is that Wordle speedrunning is usually timed from when you first see the puzzle to when you submit your answer, so it's about how fast you can think and type rather than just getting a good guess count. Some folks use tools to help verify their times since Wordle doesn't have an official speedrunning mode. You'll find communities on Reddit (r/wordle has discussion threads), Discord servers dedicated to word games, and some people stream their attempts on Twitch.
Getting started is pretty straightforward - just start timing yourself from the moment the puzzle loads. You don't need fancy equipment, just a timer or screen recording software to document your runs if you want to submit to leaderboards. The competitive aspect varies depending on which community you join. Some are super casual where people just post their times for fun, while others are more structured with categories and verification. If you're already consistently hitting 3-4 guesses, you've got the word puzzle skills down. What matters for speedrunning is pattern recognition speed and not second-guessing yourself too much. I'd suggest watching a few YouTube speedrunners to see their strategies - some folks have specific opening words they always use to eliminate letters quickly, which can shave off seconds.
The thing about speedrunning Wordle specifically is that luck plays a bigger role than in some other speedrun communities since the daily puzzle changes. You might crush it one day and struggle the next depending on letter frequency and patterns. But that's kind of the appeal for some people. Just jump into a Discord or subreddit, post your best times, and see if there's a community that matches your vibe.