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I currently have €30k in Kraken and €30k in Binance, how secure is that?

Because multiple customer data leaks happened already. Anyone can find out if you bought a Ledger or not by downloading the leaked database. You should buy it from a trusted 3rd party.
but that don't give anyone access to your ledger device.

I would not worry about using a Ledger nano S for instant to store my crypto, works well.
 
I've already emigrated from my European home country a while ago, but I'm a bit paranoid.

How secure is it for me to keep storing my €60k in Bitcoin on the Bitcoin Exchanges Kraken and Binance?

Is it really much better to move my Bitcoins to an offline hardware wallet?
Well that depends how much this is of your total net worth.
If for example you have 1M+ and make 10k month, you can forget about that take convenience over security.
If this is all you got and with no other income, I would be extra careful.
 
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I think most active crypto enthusiasts/traders have a tiered setup:
  • hardware wallet for cold storage (long term holdings, extra care to be taken)
  • metamask and the likes for hot and active trading (actively being used for trades, swaps, IDOs)
  • centralized exchanges (binance, coinbase, kraken) to trade on there
The point is to keep as little as possible in the non-hardware wallets as they should be the most at-risk. Now, you also want to avoid transferring from the hardware wallet every day to fund your trades so it's a balance only you know how to find based on your stakes and trading activity.
 
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Now, you also want to avoid transferring from the hardware wallet every day to fund your trades so it's a balance only you know how to find based on your stakes and trading activity.
No strong reason to limit transfers to/from the hardware wallet.

For incoming transfers, you just make sure to never reuse an address. You can generate an unlimited number of addresses for free, and reusing addresses is considered bad practice. I think reuse is only acceptable if the payment comes from the same source, but even then it's not smart. Addresses were never designed to be re-used. All modern wallets consolidate all your address balances for you, so you just see 1 combined balance.

For outgoing transfers, you can first coinjoin the coins so nobody even knows how much you had at that one isolated address. Note though that some exchanges don't want to grant you financial privacy and freeze coinjoined funds, so you might want to look at the mechanism employed by Samourai Ricochet. Basically, it emulates a few "normal" transactions after the coinjoin, so the recipient doesn't know if you coinjoined yourself or someone who owned the coins before you got them.

I suggest a wallet like Wasabi Wallet. The "beginner" wallets don't give you enough control. E.g., some wallets don't show you which address you are sending coins from (makes "coin control" impossible).

PS: Some authoritarian governments might consider above practices to lie in the gray area or even be illegal. Please do your research.
 
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No strong reason to limit transfers to/from the hardware wallet
You're totally right — it's moreso a convenience point that I was making! Basically, transfer enough to your hot wallets so that you don't have to use your hardware wallet "that" often.

Some peeps use two hardware wallets, one for cold long-term storage and another one for more frequent use. Really depends on the volume and convenience one seeks.