Currently have 457B + TRS (TX Retirement System for Education Professional). Should I invest in a 401k as well?

Currently 24 years old. I worked for a local education department for 2 years and contributed to a 457B. In Texas, it is mandatory for educators to pay about 8% into TRS. I stopped working at that job last year, and recently started a part time job that offers a 401k with 3% employee match. I also got offered a full time position in education and plan to continue contributing to my 457B and mandatory TRS. They do not offer 401k, and I do plan to keep my part time work (for weekends or after hours) as my full time is remote. I probably work about 8 hours a week part time.

I am wondering what would be the best move— solely contribute to 457B and TRS, or also do 401k as well. I don’t think I will plan on staying in education forever, and would like to move to the private sector within the next few years— but the future is also not set in stone.

Any advice is appreciated as I don’t really have much knowledge on these types of things. Thank you :)

EDIT: TRS - Teacher Retirement System