Fanis on Nostr: You need funds available to create a transaction that spends from the anchor output ...

You need funds available to create a transaction that spends from the anchor output and pays enough fees to get both this new transaction and the initial transaction (the one closing the channel) mined.
Your anchor output in the closing transaction spends to your funding pubkey, which is what makes it *yours*. Your node hence needs to take part in the fee-bumping transaction to actually spend the anchor output, since it's the only one able to spend it (while the transaction remains unconfirmed). The easiest way to do CPFP is hence to also have available funds on your node, which your node can add to the transaction spending the anchor to increase the overall fee.
The funds could come from an external wallet, but that means coordinating a transaction between your node and this external wallet. Additionally, having the extra-funds already on your node makes it possible to easily automate this fee-bumping process.