How secure is a network HSM connection with TLS disabled, relying only on IP ACLs and PKCS#11 slot PINs?

Specifically:

Active attacks: Could an attacker on the network still send commands to the HSM (e.g., making it sign arbitrary data) despite IP ACLs and slot PIN protection?

Unknown, but it’s definitely easier than if the system did use TLS. The pin is only protected by the used algorithm for pin transmission (which often is just plaintext).

Passive attacks: Without TLS, is the traffic between the client and the HSM (including decryption requests and their plaintext responses) visible to an eavesdropper?

Yes, this information often is just present in plain text in the packets (it depends on the exact implementation, but most I have seen rely on the TLS feature for protection against eavesdropping.

Compliance: If the network is already isolated and considered protected, would PCI DSS or similar standards still require TLS (or equivalent encryption in transit), or could this configuration be acceptable under those conditions?

I am not a PCI-DSS expert, but typically these standards don’t require a specific technology used. Just that there are mitigations against specific threats. (Which than would mean TLS in most cases, but not all). Network isolation is typically seen as a in-depth protection against lateral movement, not to ensure integrity and confidentiality of the data in use.

In other words: If the network is already assumed to be secure, does it make sense to rely only on IP ACLs and PKCS#11 PINs instead of TLS? Or is there little justification for this setup — since if the network were truly that trustworthy, the rationale for using an HSM in the first place would be questionable?

All of this depends on the threat model and what exact measures are being taken a why, for example. The HSM could be used to securely distribute and store the cryptographic secrets, making stealing the secrets hard. It doesn’t have to be used to ensure the confidentiality of the messages themselves.

There is not enough information here to draw a conclusion with, but there is enough to state that your inherent assumptions are unfounded (they require more justification than you are doing here).