Good Afternoon, Namastey !
TPS is not a visa status, but F1 is and students are allowed to work with DHS authorization (CPT, OPT or any other kind of valid EAD) ! From the information you have provided, employer is filing your GC via PERM labor certification. As long as you are legally residing or working with authorization during the process, it should not affect your application negatively since you have not done anything illegal or without permit. At the final stage of process, when you file for I-485 you need to fill out detail information about your work history and visa status, which will adjust your student status to permanent resident.
We have worked with few similar cases. if you would like to follow through and provide further details, please feel free to contact us.
Thank you, kindly
A Square Accounting Services
Phone: 406 345 5166