Good instinct to ask — a reused or low-entropy k in ECDSA really does leak the private key (two signatures sharing a k, or a biased RNG, lets you solve for d).
Two things worth separating:
1) Sparrow isn't the signer here. In a SeedSigner multisig, Sparrow is the coordinator / watch-only wallet — it builds and combines the PSBT but never holds a key and never generates a nonce. The signing, and the nonce, happen on the air-gapped SeedSigner.
2) Modern Bitcoin signers, SeedSigner included, don't draw k from an RNG at all. They derive it deterministically per RFC 6979: k = HMAC(private key, message hash). No RNG means no weak-RNG to attack, and because k is a function of the key and the exact message, you can't accidentally reuse it across two different messages. Taproot/Schnorr spends use BIP340, which is deterministic plus added auxiliary randomness — also hardened against this.
So the nonce safety in your setup comes from the signing device's library, not from Sparrow. The practical things on your side: run current SeedSigner firmware, and verify the PSBT on the device screen before you sign.