The fee rate does not depend on the wallet/exchange you are sending Bitcoins too. It's mostly dependent on the size of your transaction and the state of the mempool (if you want it to be confirmed quickly)
You can use tools like
https://mempool.space to observe the mempool and also find out what the most suitable fee rate would be for you.
Ideally, the unconfirmed transactions in the mempool
tend to drop on weekends. This in turn leads to a drop in the fee rate required to confirm transaction in the next block.
Right now, 10 sats/byte isn't bad.