Will my transaction fee be way higher because it will involve putting together multiple transactions of all my small purchases?
Discussion
No, I don’t think so because of how exchanges work internally.
What exchange are you using?
River financial but haven’t sent to cold storage yet. I think they likely batch transactions to one when I transfer.
I may be completely mistaken when it comes to River, but most exchanges have a few hot addresses to service withdrawals and what you have is a database entry allowing you to withdraw a certain amount of BTC.
Now, when you’re managing your own UTXOs in self custody you do need to take things like this into account for building transactions.