From v12, there is no online payment button available in the invoice mail template. You have to send a separated mail template through action--> share or action --> generate payment link in v13

If you want to have that link directly in the mail send to the client. You can edit the mail template and add this url in the hyperlink

${object.get_base_url()}/mail/view?model=account.invoice&res_id=${object.id}&access_token=${object.access_token}

In V13 the hyperlink is:

${object.get_base_url()}/my/invoices/${object.id}?model=account.invoice&res_id=${object.id}&access_token=${object.access_token}