This one is a bit tricky, but it's possible.

On marketing Automation, you can create a campaign of the type "email", to send the first email to the mailing lists.
After that action, you can create another activity, this time you should pick "Server Action".

Into the Server Action,  create a NEW Server action, the easiest way, I believe is to use the Execute Code directly, and have a function to create a new activity in every contact, with the current Campaign details "(Campaign name: price list sent")

Here is an example. Notice that this is just a reference.
Some changes might be necessary according to your needs:

for recipient in record.mailing_contact_ids:
    # Get contact and details
    contact = recipient.contact_id
    campaign_name = record.name
    price_list = record.pricelist_id.name if record.pricelist_id else 'Default Pricelist'
    
    # Create activity on contact
    env['mail.activity'].create({
        'res_model_id': env['ir.model']._get('res.partner').id,
        'res_id': contact.id,
        'activity_type_id': env.ref('mail.mail_activity_data_todo').id,
        'summary': f"Campaign Sent: {campaign_name}",
        'note': f"The campaign '{campaign_name}' was sent with the price list '{price_list}'.",
        'user_id': record.user_id.id or env.user.id,  # Assign activity to the user responsible for the campaign
        'date_deadline': fields.Date.today(),
    })