Transaction log backup after full backup is too big Our current production database performs a full backup daily at 7AM. The transaction log backup takes place every 15 minutes (24/7).

Database version: Microsoft SQL Server 2014 - 12.0.4100.1 (X64)
The .mdf file size: 3.9GB
The .ldf file size: 6.5GB
Recovery Model:Full
Full backup size at 7AM: 3.8GB

The transaction log files (.trn) are normally below 50MB but after the full backup (at 7AM) the next transaction Log is around 1500MB. This is an issue for me because transaction log files are being transferred across network and restore time reason.
This is the script of the full backup:
BACKUP DATABASE [DB_PROD] TO
  DISK = N'F:\SQL\DB_PROD_backup_2020_10_12_114830_1849966.bak' 
WITH NOFORMAT, NOINIT,  NAME = N'DB_PROD_backup_2020_10_12_114830_1849966', 
SKIP, REWIND, NOUNLOAD,  STATS = 10

There is a re-organize index step before the full backup. The command is like this:
ALTER INDEX [UC_LCRecipe_Name] 
ON [dbo].[LCRecipe] 
REORGANIZE WITH ( LOB_COMPACTION = ON )
My understanding is that full backups do not truncate transaction logs - only transaction log backups do (e.g., the full backup is fairly independent of the transaction logs).
However, my guess is that the re-organise all indexes does a lot of data processing - it is likely that these go into the transaction logs and are causing your issues.
You could test this by disabling or delaying the re-organise indexes one day, and see what happens to the transaction logs.