Central Electronic Module (CEM) removal instructional video for
1999-2004 S80
2001-2004 S60, V70, XC70
2003-2004 XC90

It looks like one of the air box hoses that control the hot air flapper.

Look for two fittings on the rear of the air filter box and see if one is open without a hose

There are also cruise control hoses in that area, those go under the air box , I believe

It looks like the hose attached to the device in the second photo is near to failure. The hose diameter change at the end of the hose nipple is showing failure cracks. It would be good to replace now before it fails. Soap Box Rant Alert! Everyone attempting to service a modern vehicle should periodi...

Hey, nice engine ! Without that pesky turbo pipe in the road and the collectors edition “DOHC” cover.

+1 for hose coming round that side of box being cruise vacuum motor line...
Or
From the bottom nipple of air box flap control just been tucked out of the way...

Buying parts like this on eBay is not a good strategy. Good parts are expensive , but that is how you get the “good”

There are about six different versions of the fuel pump. Did you contact a site like FCPEuro or IPD so that they could lead you to the right one? They just need the vin#. It's selling for 150-200 on FCP depending on which one it is. Not really expensive, plus you get a lifetime warranty and customer...

I’m wondering how the pump runs with no electricity

It is a pain (in my opinion) to change these fuel pumps on the P2 because of the two sump tank has a fuel pickup snaked through from one side to the other. A good reason to buy only original Volvo pumps. The 850 may have the same arrangement - I don't know. Volvo had a recall on early P2 for cracks ...

My 2004 S80 had the recall performed in 2016 for the fuel smell from a cracked pump. Not sure how recalls work in Germany, but my pump was replaced free of charge here in the States. Free is always better! Would not hurt to check your VIN # June