Does being an independent contractor count as a mini-job?

I have a work permit and a full time job in Germany.
I now want to have a mini-job on the side (450€/month).

I received a contract from another company, working ~5h/week, which does not exceed 450€ per month. However, the contract does not mention being a mini-job. It states that I am an independent contractor and am responsible for all the insurances and taxes.

Does it count as a mini-job, as long as I do not earn more than 450€ per month? My employer does not forbid me from working on a side job, there are no issues on that side.

Mini-job’s definition from wiki:

Marginal employment (German: geringfügige Beschäftigung), also called
a mini job or €450 job, is an employment relationship with a low
absolute level of earnings or of short duration.