I don’t think we’re going to see in this show any Starfleet officers committing information to personal logs that could threaten history.
SNW seems very conscious that personal logs aren’t entirely personal beyond access.
Una recorded and deleted her personal log acknowledging she is Illyrian in season one.
Later shows in the continuity have revealed to us that some personal logs to become available to next of kin, or are even studied by future Starfleet personnel.
Having Uhura pointedly resist providing the personal logs to La’an in ‘Ad Astra Per Aspera’ also underscored to us that it’s the ethics of communications officers that protect privacy.