I echo basically everything selkie said.

Active characters are collaborative characters. They act as much as players in other people's stories as they do as the protagonists in their own. This, I find, is more often than not something a writer specifically has to foster.

Be curious about other people's characters and stories! Where do you synergize? What interesting contrasts can you play on? Are there shared goals? Opposing ones? Find the hooks that you can pull on, and tug with all your might.

A mistake I see people make a lot is that they are so focused on their own stories, on their own goals and plans, that they lose sight of the opportunity to widen their horizons and try new things invited by the site plot or by other characters. They approach forum-roleplay as writing a novel, when it's actually writing back and forth with another person.

It's ping pong! They ping something at you, and you pong back.

Be open to what you receive, and do your best to give something worthwhile back. No thread is a throwaway thread, imo, if you take this approach.

Things that can help facilitate this:
-Understand what you enjoy in roleplay. Sometimes the reason your character feels 'passive' is because you aren't actually interested in the plots you've designed them for. Your muse knows what's up. No shame in being self-indulgent!

-Read threads you aren't in. You'll be amazed at how many incredible stories are written all around you, and often people are kind enough to share them with you.

-Be the one who initiates for plots, and keep an open mind. Come to people with specific ideas that show you have an interest in their character, and explain why you think the plot would be fun for both of you. Be sincere and thoughtful in this, and likewise, be open when new people offer the same to you.

-Have clear character motivations and goals. This will make it easier to "push" things forward. Often, your character will have many motivations! And different ones will appear in different scenarios. These should include capital-G goals ("I want to avenge my parents") and also lowercase-g goals ("I want to get better at making friends").

-Have an understanding of your character's day-to-day routine. This sounds boring, but it's so helpful. Where does your character work? How do they blow off steam? Do they go on daily walks somewhere? Are they doing any hobbies? This becomes an easy entry point for a lot of new threads!

-Be flexible. Take the "yes-and" approach to roleplay, always. Instead of saying, "My character never does X," ask yourself, "What would it take for my character to do X?" That's a more interesting question, and more fun one to write the answer to. If you want to join a raid, find a reason your character would do so! It's better than sighing at your computer with FOMO. Which brings us to...

-Hold no expectations. They are the thief of joy. Write because it's fun to write! If you write because you expect a certain conclusion, you will find yourself frustrated when unforeseen difficulties arise (ie, people lose interest/go inactive/the site plot doesn't go how you want/someone else gets the canon position you want/etc.). That will take the wind out of your sails, but worse, you might find yourself writing with the destination in mind instead of enjoying the journey. Many of my best plots have been organically developed through genuine interest in exploring connections between characters, and I never expected where they would lead.

-Be kind. No one is obligated to write with you as a hobby. Make the effort to be a friendly and gracious roleplayer, and you'll find more doors open to you.