You can get sued for omitting such a page (by any bored lawyer really) because it's considered anti-competitive and a misdemeanor: https://de.wikipedia.org/wiki/Impressumspflicht#Ordnungswidr...
Here's a lengthy explainer of what should go in a privacy policy to be fully compliant (in German), note that "clear and precise" language is generally understood to mean being explicit about the legal basis (i.e. parts of the GDPR) under which the data is collected and processed: https://www.datenschutz.org/datenschutzerklaerung/
In any case, your privacy policy link on the German language version of your website gives me the policy in English, which violates the GDPR's requirements for "clear language" regardless of the actual content by not being in German: https://voicedocs.com/de/legal/privacy-policy
But to be honest, you shouldn't be asking a random person on HN, you should talk to a lawyer.
The privacy policy also doesn't provide all the information the GDPR generally requires you to provide, e.g. spelling out users' rights under the GDPR and what legal basis is given for collecting each specific piece of information.
I'm mostly pointing this out because it could get them sued, but I'd also expect a company based on a service like this to take privacy a bit more seriously, or at least present themselves as if they do so.