What is the part below the solenoid on a Honda Element? Error P2647?

Car: Honda Element, 2004, VTech Engine

Symptoms: Stumbles on acceleration (notably higher RPMs)

Otherwise, drives fine.

Check Engine Light with Code: P2647, stuck rocker arm.

I've found a lot of great articles on this error and so I started by removing the solenoid. After removal, a large bolt (1"+) below it was exposed with a hose that was most likely connected. The hose has some plastic in it that appears broken and the bolt also has some plastic on it that appears broken.

Anyone know what the hell this part is or what it does?

Would this cause the stumbling?

Should I still replace the solenoid?

Thanks in advance for your advice.

(p.s. don't tell me to take it to a mechanic unless it's s joke

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