European plug – Polarity important in Thailand ?

Hello, I live in Thailand and I just bought and espresso machine and a grinder that have a European plug with 2 round pin and 1 ground hole. In Thailand wall sockets have no ground pin, so the machines are not grounded when plugged. I have attached the pictures of both plugs and the socket.

1) If used ungrounded, the plug can be inserted in the wall socket in both directions. Are both directions safe to use or should I insert it in 1 direction only? The wall socket has L on the left, N on the right and ground on the top.

2) Should I be buying an adapter that adds a ground to the plug? Here is one I found: https://www.toshino.com/product/ea-of/

Thanks a lot in advance

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