Hi Hendrik,
thank you very much, your code is what I also was looking for!
I want to share my improvement. It is only to add both emails, the one from the invoice person and also the one from the company.
class ResPartner(models.Model):
_inherit = "res.partner"

invoice_emails = fields.Char(
string="Invoice Email", compute="_compute_invoice_emails", store=False
)

@api.depends("child_ids.email", "child_ids.type", "email")
def _compute_invoice_emails(self):
for partner in self:
contact_ids = []

# Includes company ID if has email
if partner.email:
contact_ids.append(str(partner.id))

# Includes contacts IDs type invoice with email
invoice_contacts = partner.child_ids.filtered(
lambda c: c.type == "invoice" and c.email
)
contact_ids += [str(contact.id) for contact in invoice_contacts]

# Remove duplicates (if there are) and join
partner.invoice_emails = ",".join(sorted(set(contact_ids)))

Just wanted to add a comment (I cannot edit nor delete). It works in Odoo18 and I changed the name invoice_ids for invoice_emails (I thought invoice_ids can be used by Odoo and so I wanted to avoid problems). Therefore, the code for the Email template is {{ (object.partner_id.invoice_emails) }} .