Sorry for the late reply
Those are indeed the stems. Inside there will be parts that move when the coil is powered. They look to be one piece, but you can open them up.
New O rings and stems can be bought from Bobcat, but napa is a better option for orings.
If you turn the ignition on, activate the aux hydraulics and move the thumb switch, you should be able to feel the stem buzz in your hands with the coil on it. Ensure both do this, if one doesn't, it is probably bad. but try it on the other working coil if that' the case to ensure it is indeed different.
if when powering up does it bog down only when u engage the grapple or every time now, if it bos only when u engage then u have a problem with the engage valve not opening, possibled solenoid not opening, elect supply proble,. if it is trying to open and not succeeding then u have a stuck spool, put your hands on the hoses on each side of the cylinder, does the hose stiffen, if both the open and close side stiffen the you have 2 valves open essentially trying to engage both open and close the hydraulics, could be an open o ring or an electrical solemoid hanging open , this gives an identical result, this put power to both sides of the hydraulic system essentially pitting the hyd system against itself, cracck the fitting on each side of the appropiate cylinder during these test, if you have flow go to the spool supplying that cylinder, if this problems are in all cylinders, then look to the power beyond valves, brek your problem down to manageable pieces, its like the question, can u eat a whole ham, ?? the quick answer is heck NO!!, the country boy answer is ahh, yeah, let me get a loaf of bread, some mayonaise and some red koolaid, make sandwiches,, knowledge is power, u know your pump is working, find where the oil is trying to go, my guess is you have a stuck valve holding both sides of a valve open , or yoy have an electrical problem trying to engage both sides of a vaklve, since it did work, um also a bloown o ring essentially trying to engage both sides also, ok forgot, detritis getting into a spool holding it open resulting in both sides trying to service both sides of the system, sorry i do run on, ramble, buck, have fun, i think you have a contaminated iol supply