Let's take coinbase as an example. Can someone (except coinbase) trace my coins if I send them to an exchange address and then send it to another address? I always see that the funds on incoming transactions are sent to another address and combined with many others. On outgoing transactions there are also many inputs and this should it make hard to trace it.
So, can someone tell if I sent the coins from one address through coinbase to another address?
Technically it's possible, but the more "mainstream" and smaller your transaction is, the more likely it is that it can't be traced directly. If you make a huge transaction of a rarer coin/token to the exchange and then withdraw the same amount, it would be pretty easy to trace it.