What I understood is you came here in F1 visa and applied for H1B while still being in the US, right? If I understood correctly, you don't have H1B visa yet. You only possess valid I-797 approval notice of H1B. It is clearly mentioned on it that this notice is not a visa. So, if you are intending to leave US and re-enter later, you need to get your valid passport stamped from US embassy in Kathmandu, Nepal.

Now on expired passport issue, I don't know where you got your information from that one could travel and enter any foreign country with expired passport. It has nothing to do with this administration. You always need to have a valid passport irrespective of other documents. Entry with expired passport was never allowed, period.