The SSD runs its own proprietary firmware that controls the raw disk device itself. If it wants to insert a blob of code into your bootloader or grub2 that can do keystroke interception on a full-disk-encryption unlock, it can. This is the same idea as a technique used by intelligence agencies with a typical "evil maid" attack.

Ah yes, if you execute unsigned code from it then that's definitely possible.

Signing the code doesn't help. Where are you reading the signature-verification code from?

Presumably you use TPM and the various trusted boot technologies.

I think you’ll still have the problem with this thing being on a pci-e bus though.

Yes, I was more curious if a malicious actor (the hard drive) with access to the nvme bus could manage to exfiltrate data directly via the network interfaces without involving the OS.

I suggest you look into TPM and the full signed-code architectures it enables.