The answer actually depends on your phone model, but in theory you can use both physical and eSim at the same time if your phone supports it. They will both work as normal.
But I don't advise this. It becomes kind of pointless if you receive a text or phone call or use your home Sim you will pay roaming charges. If you're happy to do this then there's not much point getting esims in the first place as you could just use roaming.
I always remove or deactivate my home Sim and only use the eSim. I use Facebook or WhatsApp to connect with people back home. I understand this isn't the case for everyon, but standard calls and texts are really obsolete these days.