Of course, it's safe if the whole thing works on the new device, in fact you made a wallet/s recovery and the old laptop can only represent an additional risk.
Not exactly. In this particular case, OP didn't need to recover his wallet from seed. His Nano X works and holds the seed and private keys. He only changed his laptop. By installing Ledger Live on the new laptop, he would only need to connect the already preconfigured Nano X. After installing the needed coins and scanning his accounts, his balances would be updated. The seed was always in the device regardless the change of laptop.