First log backup after FULL taking lots of space
Taking a FULL backup won't clear out the transaction log entries (unless the database is in SIMPLE Recovery Model). So whatever changes take place between your last LOG backup before the FULL backup (@ 4:30 AM), and the first LOG backup once that process is over (@ 6:30 AM) would be included in that 6:30 AM LOG backup. That is a 2 hour span (you typically do a LOG backup every 30 minutes otherwise) in which you, at the very least, run index maintenance via the IndexOptimize stored procedure.

If you want to test this out, just temporarily disable both the "IndexOptimize" and "Database Integrity Check" steps (meaning, if you are using the CmdExec step type so it can call SQLCMD, just add REM to the beginning of the line in both steps). Let that run for one night and if I am right, it will be very obvious. Then, remove the REM from one of the two steps so that only one of them runs again (maybe start with the "Database Integrity Check" step) and let that run for one night and then you should see how much impact each of those first two steps has on that "first" LOG backup.

If the "Database Integrity Check" step is taking up more than a small portion of that LOG backup, then you might be able to split that initial backup into two (even if not an even 50/50) by doing a LOG backup after the "IndexOptimize" step. If all (or most) of the LOG backup size is from the "IndexOptimize" step, then maybe try to schedule a LOG backup for 4:36 AM to attempt to cut the resulting LOG backup in approximately half (given that you show that first step running for just under 14 minutes).