I have many bitcoin addresses with small balance leftovers <0.001 BTC.
Sending it as one tx will be against privacy, right?
Yes. There is no way for you to consolidate all the small UTXOs unless you spend all of them in a single transaction. If you want to have some form of privacy, you can possibly try to segregate them from each other and only spending the UTXOs that are associated with the same addresses/ a small group of addresses only.
Additionally, when I need to send bitcoin I need it to be confirmed quickly mostly, and if I want that my tx to be confirmed quickly I need to set high fee rate, and if I have many inputs this fee will be incredibly high.
So I think I can try to merge it now, but how to do it better to not harm my privacy?
That is inevitable. Consolidation transactions are best done when the fees are relatively low so that it can be confirmed sooner. If the fees are consistently high, then it'd be better for you to spend specific UTXOs for the transactions that you're making.
The only way for you to preserve your privacy, when spendlinking is inevitable is to consolidate and send them to a mixer or use CoinJoin. If not, then it'd be better for you to use each of the inputs individually.