Word that means earliness and lateness at the same time

Unscheduled:

: not appointed, assigned, or designated for a fixed time : not scheduled
// made an unscheduled stop
// unscheduled visits

While strictly speaking the package in the example sentences might have been scheduled for a different time, the time of its actual arrival was unscheduled.

The sentences need to be rephrased slightly for this:

• I was expecting my package tomorrow and it arrived today. The package's arrival was unscheduled.
• I was expecting my package yesterday and it finally arrived today. The package's arrival was unscheduled.

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The use of the noun could also be more idiomatic in this particular set of sentences:

• I was expecting my package tomorrow and it arrived today. The package's arrival was not according to schedule.
• I was expecting my package yesterday and it finally arrived today. The package's arrival was not according to schedule.

I suggest unpunctual.

Unpunctual (adj): Not happening or doing something at the agreed or proper time.

Example: The trains into Tbilisi were notoriously unpunctual. [Lexico]

In your example:

I was expecting my package tomorrow and it arrived today. The package was unpunctual.

(Unforeseen in some similar contexts could also be used.)

You could describe this as ill-timed, which indicates that something did not occur at the suitable or correct time. A similar choice would be untimely, which also expresses that the timing was not correct. Neither of these indicate whether the timing was early or late, only that it was wrong.

Both of these carry some connotation of misfortune or particularly bad timing, rather than simply a missed schedule. A package that arrives a day early might be ill-timed if you're not home to sign for it, but otherwise it would normally be a good thing to get a package early, so I wouldn't describe an early package as ill-timed unless there was some bad outcome that resulted from its earliness. Similarly, "untimely" often is used to refer to unscheduled things that happen unexpectedly at a bad time, as in the phrase "untimely death", and will be more often used to refer to things happening earlier than one might want .