Extract insertions that failed because of size limit from SQL Server Express Transaction Log
The size of the Transaction Log is just due to its normal growth pattern based on the amount of data that's been transacted between backups. It'll grow to whatever size it needs to hold transactions until a backup is taken on the log which flushes those hardened transactions BUT does not shrink the log file. Rather that space remains as reserved empty space that the Transaction Log will re-use for new transactions.
So there is no correlation between the log file's size and if your failed to insert data is in it. At best it may be in one of the previous backups of it, as a rolled back transaction, and in a non-human readable form. Unfortunately that failed data insert is likely gone, at least in the context of this question.