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
Email: asquare.acctservices@gmail.com
Phone: 406 345 5166

F1 to eb1 or eb2 NIW is way to go if you have few publications as an PhD koz its easy and independent . TPs is only good for those who cannot peruse higher degree and get hired in their related field . Being on tps is safe and relaxing for 8 years at least but you have to understand, its not taking u nowhere .

Thank you for the responses.