First we have to caveat this that "transactions" are a function of a particular engine. InnoDB is the primary engine used by people so I'll focus on that.
Yes, certainly there can be multiple transactions, because if there wasn't you would never have deadlocks.
But the binlog doesn't include anything that wasn't committed:
Binary logging is done immediately after a statement or transaction completes but before any locks are released or any commit is done. This ensures that the log is logged in commit order.
So by necessity, the transaction log is inherently serialized.
MariaDB has some InnoDB documentation that includes this:
You can modify data on a maximum of 96 * 1023 concurrent transactions
that generate undo records. Of the 128 rollback segments, InnoDB
assigns 32 to non-redo logs for transactions that modify temporary
tables and related objects, reducing the maximum number of concurrent
data-modifying transactions to 96,000, from 128.000. The limit is
32,000 concurrent transactions when all data-modifying transactions
also modify temporary tables.
The purpose of the log is to be able to recover from a catastrophic loss, by being able to replay completed statements and transactions. If recovery goes through the transaction log and a transaction is never committed, that transaction isn't in the transaction log.