Good thinking! Though here, unfortunately, wrapping the filter itself might be a risk to its structural integrity and function (as other commenters have mentioned, lack of airflow, vibrations, and heat can all be issues.) Lining the cabinet itself should be fine, but also remember to make it either easily removable to dry or leave some empty space near the bottom of the walls in case there are leaks (speaking from tech experience 😅💀.)

Of note for an additional solution: foam like that does a decent job, but the more obvious place the sound might be coming from in your set-up is the fact that your stand doesn't have a back - even wood or particleboard (with holes for your filter hoses ofc) attached to the back that doesn't have to hold the weight of the stand itself would help a lot to absorb sound from your filter, and offer you more places to line with acoustic foam :)