Domestic travel during H-1B 60-day grace period - any issues with ICE/CBP?

I’m currently within my 60-day H-1B grace period after my employment ended.

My H-1B visa stamp has expired, but my I-797A has an I-94 that is valid well into the future.
I’m considering taking a domestic flight within the US while I’m still within the 60-day grace period. Has anyone here traveled domestically in a similar situation?

Specifically, I’m wondering:
Did you encounter ICE/CBP or any immigration checks at the airport?
If you were questioned, was showing your I-797A/I-94 and explaining that you were within the 60-day grace period sufficient?
Is there anything else you would recommend carrying?