Other types of backups shouldn't break the restore chain unless they are specifically configured in a way to do so. For example, I just ran into this issue with Veeam and it managing my Transaction Logs externally which was stepping on my maintenance plan I had running to backup the Transactions Logs internally. You can find more information about that in this StackExchange answer.
Long story short, Veeam has an option (stupidly) to blatantly delete the Transaction Logs, which was how a former member of our infrastructure team setup Veeam. This was breaking the restore chain for me. Turning off that setting was the fix, especially since I had maintenance plans natively managing my backups in SQL Server.
Also, why are you taking a Differential Backup at the same time as your Full Backup? Differential Backups are meant to capture the differences since the last Full Backup (or since the last Differential Backup). You'd be better off doing that later on, like mid-day, or hourly if you want to switch your Transaction Log Backups to be more frequently too.