If I change the user status manually using the backend the modification date (lastupdatedate) is not updated

That's not a bug and is working as intended. That only updates when the user themselves modifies their profile.

nor is acceptedtermsconsent

Also working as intended. You can not give consent on another users behalf. That would go against GDPR, which is what it was implemented for.

Users often call me or send emails to confirm their subscription.

Then I recommend fixing your sites flow so users do not need to call you, but can instead do this themselves. Confirmation, terms and conditions, etc.. is an entirely automated process that should not require moderation.

Also, Acymailing users already registered are approved but if the user register in CB his status is not updated. A manual intervervention is needed. But the record modification date is not written on the database!

We do not integrate with AcyMailing Users so I do not know what to tell you in regards to this.

Use CB Profile Update Logger and within its Parameters tab set "Backend" to "Enabled". You will then have full profile data change logging for frontend and backend. It can even send a notification about changes as well. We've no plans at this time to hardcode in other modified date fields.

You can also use CB Auto Actions to update the lastupdatedate field if you wanted, but I don't recommend doing that as it's meant to indicate the user themselves has updated their profile.