@Ray Carnes: Thank you for your reply.
I'm adding this comment to my post, instead of your answer, because for some reason it's not allowing me to.

I'm trying to check the request-logs via Chrome's developer bar, to see which requests are being done.
That gives me some clarity, but not all the way. For example, I don't see where / how requests are getting their input from. I can guess based on other API requests that are done, but this way of working will cost me hours if not days to completely find out how to do it.

I have an implementation (made in 2022) in our codebase that works for Odoo version 17. I'm not sure if I can keep this for version 18 with some small changes here and there? When I compare what I see in my codebase (for version 17) it does have quite a lot of differences with what I see in the request logs (when connected to a trial (v19) environment).

For what it's worth, here's the (PHP) implementation that I have for v17:

$invoice = $this->accountMoveRepository->find($this->invoice->external_id);
if (! $invoice) {
throw UnableToSendInvoiceException::invoiceDeleted();
}

try {
// Ensure invoice is posted.
$this->accountMoveRepository->update($this->invoice->external_id, ['state' => 'posted']);

$actionSendAndPrint = $this->odoo->api()->call('account.move', 'action_send_and_print', [(int)($this->invoice->external_id)]);
if (empty($actionSendAndPrint['context']['default_template_id'])) {
// This exception is being thrown when connected to Odoo v18
throw UnableToSendInvoiceException::unknownDefaultTemplateId();
}

$response = $this->odoo->api()->call(
'account.invoice.send',
OrmQuery::CREATE,
[
[
'invoice_ids' => [(int)$this->invoice->external_id],
'composition_mode' => 'comment',
'template_id' => $actionSendAndPrint['context']['default_template_id'],
'is_email' => true,
],
],
[
'context' => [
'active_ids' => [(int)$this->invoice->external_id],
'active_id' => (int)$this->invoice->external_id,
'active_model' => 'account.move',
],
]
);

$this->odoo->api()->call(
'account.invoice.send',
'onchange_is_email',
[(int)($response)],
[
'context' => [
'active_ids' => [(int)$this->invoice->external_id],
'active_id' => (int)$this->invoice->external_id,
'active_model' => 'account.move',
],
]
);

$this->odoo->api()->call('account.invoice.send', 'send_and_print_action', [(int)($response)]);
} catch (RemoteException $e) {
throw OdooUserApiException::fromRequestException($e);
}