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>I’ve got a trezor and I was playing around with another wallet and entered my seed phrase.
Now, your seed phrase is no longer considered hardware secure. Putting your seed phrase into a software wallet defeats the entire purpose of a hardware wallet. Everyone here will recommend that you start over with a new seed phrase now.
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>I could see my coins on my wallet but I’m wondering, would I be able to transact with those coins without needing to approve transactions on trezor device?
That is correct. Now that you are using a software wallet, you are no longer protected by the Trezor and therefore do not require approving on the Trezor.
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>Does the approving transactions on trezor happen when using the device?
If you are using Trezor (only the Trezor and not a software wallet), the signing all happens on the device. The seed phrase and private keys never leave the device. This protects the seed and key from viruses and keyloggers.