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Are there VPN providers that do not require such KYC?

Yes. mullvad onion, but I wouldn't use it for a node because they don't have port forwarding anymore. You can tailscale through a VPS and njalla onion lets you rent it anon w/ bitcoin.

How can I fund my node with a part of my stack which might contain previously tainted coins due to having already been used for running an LN node.

Mix them. See: #296379 - I use something similar to this pattern too.

How to open channels in a private way? Taproot-related, etc?

I'm mostly using segwit only as last time I checked, most channels were still segwit - bigger anon set = better.

I used to use amongst others Wallet of Satoshi to move off-chain liquidity back on-chain. Is that also a possible attack vector in determining my node's identity?

Only if you also send back to your own LN node. What I've used in the past is submarine swap out -> wasabi -> new channel.