Unfortunately, there is no current way to directly see your library on the Epic Games website. However, you can instead look at your transaction history to see which games you have on Epic Games. All of your owned games will appear in the transactions list under the purchase tab, even if the game was free like Valorant.
1. Go to the Epic Games website and click the profile icon.
2. Sign in to your Epic Games account.
3. Go to your profile icon and select Account.
4. Select Transactions from the side menu.
5. Check the description column for the games you own.
Find a Specific Game
You can press Ctrl and F on your keyboard to open the find menu. This can be used to search for a specific game. If the game is found then it will become highlighted and you will automatically be directed to its location in the list. Additionally, you can press the Show More button at the bottom to see more games and transactions.
How to See Your Epic Games Library on Mobile
1. Go to the Epic Games website and open the burger menu.
2. Click the profile icon.
3. Sign in to your Epic Games account.
4. Open the burger menu, press the profile icon, then select Account.
5. Go to Transactions.
6. Check your games in the Description column.
Conclusion
Although not the best solution, viewing your transactions page does allow you to see what games you have in your Epic Games library. This allows you to check your games through your browser on a computer and your mobile device. Provided you are signed in to your Epic Games account this can be done fairly quickly. Being able to use the find feature further speeds this up, allowing you to search for games if needed.