If I was a full time employee while being a full time post graduate student, does this impact my tax situation?

One situation doesn’t affect the other. 

There is a filing requirement. If you are over that amount, you will pay taxes on the amount over and above. Being a student does not relieve you of the obligation. If you are still somehow being claimed as a dependent, that could affect you.

 

Filing Requirements

 

• Single filing status:
  • $12,550 if under age 65
  • $14,250 if age 65 or older
• Married filing jointly:
  • $25,100 if both spouses under age 65
  • $26,450 if one spouse under age 65 and one age 65 or older
  • $27,800 if both spouses age 65 or older
• Married filing separately — $5 for all ages
• Head of household:
  • $18,800 if under age 65
  • $20,500 if age 65 or older
• Qualifying widow(er) with dependent child:
  • $25,100 if under age 65
  • $26,450 if age 65 or older

Dependents – If you can be claimed as a dependent by another taxpayer, your standard deduction for 2021 is limited to the greater of: (1) $1,100, or (2) your earned income plus $350 (but the total can't be more than the basic standard deduction for your filing status).