There are three main websites where people play Connect Four competitively: Papergames, Board Game Arena, and Flyordie. Each has a different feel depending on what you're looking for.

Papergames

Papergames.io (often called PPG) is the most active community. You'll rarely wait long for a game, which makes it the best place to grind out reps and get comfortable with different positions.

The skill level is mixed — you'll face everything from complete beginners to strong players. This is a good thing if you're learning, because you get practice against a wide range of styles.

This site also integrates with the analysis tool — you can paste any Papergames game link to review it move by move or link your account directly.

Board Game Arena

Board Game Arena (BGA) is less active than Papergames, so you may wait a bit longer for matches. The trade-off is that the average player tends to be slightly stronger.

Flyordie

Flyordie has some of the strongest Connect Four players online. The community is small though, and finding a game can be difficult — especially outside of peak hours.

If you're specifically looking to test yourself against top-level players, this is where they tend to be.

Discord

The Connect Four Marauders Discord server is where the competitive community organises. If you want to play against strong opponents directly, ping the practice ping role in the #practice-board channel to find a game.

The server is also a good place to ask questions, discuss strategy, and find resources for improvement.