How to permanently remove persistent hackers from a compromised Mac?

Beyond the intro to the issues requested above…

Given your report of the remediation steps tried, and failed,

• and given you have undoubtedly performed the compromised-account steps,
• have given you have enabled a recovery key and enabled security keys,
• and given you have undoubtedly already tried lockdown and that too failed,
• or you’re either potentially misinterpreting something benign such as log chatter or an expected Apple feature, (this is centrally why Mac Jim ID asks for information about what is or is not happening)
• or you’re getting exploited or gaslit by somebody local and with access to your passwords and security keys and equipment,
• or your attackers are immensely well-funded and immensely capable and well outside of what anyone around here can assist with via forum postings.

Barring some comparatively simple and direct local case from the above or similar, this including confusion about Apple features or understandable the usual ominous or scary wording in telemetry including utterly normal references to Pegasus, …

… your remaining option is to sell your Apple gear and revert to using security-hardened gear more suited for someone that is apparently an immensely-valuable target, and to accordingly rework how you store and secure and access your dats.

Multiple password changes and multiple resets and related remediation and recovery failing puts this well outside of what folks here can assist with, too.

What exactly are you seeing and where are you seeing it? Feel free to include screenshots to visualize what you are seeing as long as it does not include any personal information.