Hello,

You can use an automation rule:

• Model: Message (mail.message)
• Trigger: On create
• Apply on: Related Document Model = helpdesk.ticket
• Action: Execute Code

mt_comment = env.ref('mail.mt_comment', raise_if_not_found=False)

if (
    record.model == 'helpdesk.ticket'
    and record.res_id
    and record.message_type in ('email', 'comment')
    and record.subtype_id == mt_comment
):
    ticket = env['helpdesk.ticket'].browse(record.res_id).exists()
    if ticket:
        author = record.author_id

        is_internal = any(not u.share and u.active for u in author.user_ids) if author else False

        target_stage_name = 'Answered' if is_internal else 'To be answered'

        target_stage = env['helpdesk.stage'].search([
            ('name', '=', target_stage_name),
            '|',
            ('team_ids', '=', False),
            ('team_ids', 'in', ticket.team_id.ids),
        ], limit=1)

        if target_stage and ticket.stage_id != target_stage:
            ticket.with_context(tracking_disable=True).write({
                'stage_id': target_stage.id,
            })

Disclaimer: I tested this solution in a standard Odoo 19.0 database. This server action looks for stages named exactly "Answered" and "To be answered". If your Helpdesk teams use different stage names, you must update those strings in the code. Be sure to configure the "Apply on" filter in the automation rule to avoid performance issues. As always, test the automation in a staging environment before deploying it to production.