When it has piled up past what will sign
Buy a little every month for a few years and you have hundreds of UTXOs. Try to move them in one transaction and the hardware wallet runs out of memory and refuses to sign. This works out which problem you actually have first — usually it is a wallet setting rather than the number of inputs — and if you do have to split, how many go in each batch.
If the device showed you an error message, start with when the Keystone won’t sign and work out which one it is. It may well not be a size problem at all.
This does not build the transaction for you. Your own wallet already does that well. What happens here is diagnosing why it breaks and working out how many to split it into.
Both the xpub and the PSBT are handled inside this browser only — there is no server to receive them. What does leave is the addresses whose balances get looked up, which go to an explorer. That is true of any wallet you use, and it is the one exposure that remains.
What do you have?
A pairing QR contains an extended public key (xpub). It is not a private key, so nobody can steal with it — but it opens up every past, present and future address of that wallet, and the balance history of all of them.
The xpub itself never leaves this browser. But looking up balances means the derived addresses do go to an explorer — and that company then knows those addresses belong to one wallet. That is the real exposure.
For what it's worth, BlueWallet already does the same thing against its own servers. It is still one more party knowing. If that bothers you, use the PSBT route instead — no addresses leave there.
We can work through it together over a screen share. Your private keys and seed phrase never reach me under any circumstance — I watch your screen and tell you what to press. Anyone who asks to see your seed is stealing from you.
What you send passes through a server once so it can be delivered as email, and is not stored. Unlike the tools on this site, contact needs a server — there has to be somewhere to reply to.