Firstly, since you've mentioned Community Edition - Odoo Studio is a feature available to Enterprise instances only. So, unfortunately, 'We recommend applying modifications to standard views through inherited views or customization with Odoo Studio' does not apply to your setup.

Secondly, a sustainable way should always equal a module development - no matter what version or edition.

About 'any tips that can bring me in the right direction' - you don't need much to extend a report.

A folder with this structure should be sufficient for the beginning:

<company_name>_account_report/
-- __manifest__.py
-- __init__.py
-- views/
-- -- report_invoice.xml

__manifest__.py needs to specify the path to the report extension (views/report_invoice.xml) and a dependency on the Invoice module as 'depends': ['account']

__init__.py can remain completely empty

views/report_invoice.xml will be something like

<?xml version="1.0" encoding="UTF-8" ?>
<odoo>
    <template id="report_invoice_document" inherit_id="account.report_invoice_document">
        <xpath expr="..." position="...">...</xpath>
    </template>
</odoo>

Now, for the detailed content of the manifest-file you can refer to literally any module in your addons directory as every module needs one. https://github.com/odoo/odoo/blob/18.0/addons/crm_sms/__manifest__.py is a really trimmed down example.

Concept of inheriting reports/templates can be seen for example in the l10n_cz module, which extends exactly the report you're looking for: https://github.com/odoo/odoo/blob/18.0/addons/l10n_cz/views/report_invoice.xml#L3

To successfully build or change a PDF report you will however have to invest your time into the documentation, chapters such as https://www.odoo.com/documentation/17.0/developer/tutorials/pdf_reports.html should bring you on the right track. Some knowledge about what XPath is and how it works and interacts with existing templates will be required as well: https://developer.mozilla.org/en-US/docs/Web/XML/XPath

Thanks. It seems I need to have a look into creating modules, as, it seems I understood the concept wrong. In my mind I need to create a new module when I want to have new functionality. It seems I need to build them (at least a bare minimum) when I want to extend stuff.

sorry, I looked into developing/extending odoo, but as this is not my main job, knowledge fades away.

Thanks for giving me the direction! I will report back with the progress.