Power steering issue

[zuvarak]

Greetings everyone

I noticed some strange behavior and didn't find anything relatable on the Internet.
So, basically, sometimes, when starting the car, the power steering refuses to engage, meaning I'm ended up with heavy steering. It's resolved by turning the car off and on again. Sometimes it takes more than 1 try. I checked the fluid level and it seems to be okay.
It never happens during drive, only when starting the engine.
Any ideas?
Could it be related to the battery? I know the previous owner changed the battery during some point but it's definitely not the original AGM.

Thanks in advance.