Good post from neerman. Spot on. You will violate H1B if you use your TPS EAD card to work somewhere while still on H1B. But you can keep the EAD card with you as a backup without issues. If you have H1B time left (2 years at least as neerman suggested) apply for GC from it. Even if you want to switch employers, try doing it via H1B still. If you want to switch to something completely different from what you are doing currently, then an H1B transfer may not be possible/allowed and you can switch to using the TPS EAD. Consult a good lawyer in this case.
One jhanjhat of being on TPS -> you cannot travel outside the country as smoothly as you can on H1B. You can via advanced parole but it has to be need/emergency-based and it can be restrictive time-wise. Also you will have to wait for them to approve, may have to provide evidence of urgency, etc. So stick to H1B if you have at least 2 years remaining. Nepal ko GC process current nai hunuparne ho.