In most organizations, vacation days are usable at the employee's discretion, up to a certain yearly limit. Days off is a more informal phrase that includes a variety of kinds of paid-not-to-work days, including sick leave, maternal/paternal leave, floating holidays, national holidays, etc. Vacation days are a subset of days off.
"Vacation days" or "days off" - English Language & Usage Stack Exchange
There's also the perennial question of whether the last day ends on the multiple of 24 hours from the time when the deadline was given, if it means midnight of that day, or closing time of that day, or what. And does "7 days" mean 7 calendar days, or 7 business days? Etc.
The form must be filled out within 10 days before the flight. Fill out the Entry Form within 10 days before your flight. What is the meaning of within in these sentences? Is it before 10 days before the flight? or Is it after 10 days before the flight? I.e. 8 days or 5 days or even 1 day before the flight is ok (even the same day as the flight)?
So when we say 'the past few days' we mean the complete set of 'past few days', not just some of them, and which means this time phrase matches the tense. Do we use the phrase 'past few days' on its own? Highly unlikely, it lacks a sense of which days.
meaning - Past few days or the past few days? - English Language ...
In Australian English, "in the upcoming days" sounds strange. "In the coming days" is acceptable but probably too formal, I agree with @BoldBen's comment that "In the next few days" is a better choice. "In the next couple of days" also works, and arguably implies a slightly shorter time frame (the next few days could be 1-4 days, whereas the next couple of days probably means 2-3 days)