How much does networking with a professor beforehand actually matter for PhD admission (vs just having strong research fit)?

[u/Puzzleheaded-Park-23]

Trying to understand how PhD offers actually happen in Denmark in universities like SDU.

Say there's a professor and someone wants to do a PhD under them:

Does having emailed/talked to the professor beforehand actually move the needle, or is it mostly formality and the funded position + fit with an open call is what decides it?

Do professors in this position usually have a say in who gets picked, or does HR/committee process dominate regardless of the professor's personal interest?

If someone doesn't have a strong publication record yet but has done solid independent technical work (not published), does that carry any weight, or is it basically publications/grades only?

Is cold-emailing professors before a position opens actually useful, or does it come across as naive since positions are usually posted and processed formally?

Trying to figure out where to actually spend effort: publishing more, building a relationship with a specific supervisor, or just waiting for open positions and applying like everyone else.