TLDR: they won’t mess up your equipment but they surely can wreck your ability to enjoy being outdoors during times of heavy infestation.
I just came across your post and I’m a seasoned veteran battling against the spotted lanternflies since 2018. Number one word of advice, if you have any tree of heaven on your property get rid of it (hack and squirt to kill the roots - refer to that Penn State guide). That is their favorite host tree from nymph to adult. I had a sapling next to my foundation this past summer and was shocked at how many were on it! My neighbor across the street had 15 of them removed this past summer (also a pool owner). As you probably know they migrate to different plants/trees throughout their lifecycle and are a very mobile pest which unfortunately makes eradicating them impossible.
Your only option is to target them during different stages of development (see Penn State guide). Smash the egg masses now that you can reach before the end of April (however most egg masses are laid up higher in the trees and way out of reach). Since you have already experienced them, then you have a good idea of which trees they flock to in your yard so consider treating them after bloom with a pesticide or using circle traps. The first couple of years I had my trees treated with a systemic pesticide to kill them after feeding but within a week more would just keep showing up from across the street. Eventually I just cut down my most problematic trees (3 river birch and 1 willow).
I still get them here by me and after 5 years now, there was a noticeable decline this past summer but their numbers can fluctuate depending on the month and weather and even the time of day (they are not active at night and will rest till daybreak). Cold weather makes them very slow (and easier to kill) but hot sunny weather makes them very active.
With this mild winter I anticipate a high hatch rate this spring. Mating season is end of August and September in my opinion is the absolute worst! As far as weather goes, they love hot and dry but will just stay on the trees in the rain (can’t fly with wet wings so that’s a great time to spray them with something or just smash them). You can step on them (approach from the front otherwise they will get away). I find fly swatters work the best and keep a few swatters out on my patio and around the pool.
The nymphs were never much of an issue for me as far as enjoying my pool goes but once they become flying adults (end of June), they start encroaching on my pool, patio and deck. They don’t sting or bite (amen) but they are a real nuisance and have a habit of jumping right at whatever vertical objects they see which includes people. If they land on the ground they crawl until they reach something to climb up (patio furniture, umbrellas, your leg). Many times they crawl along my patio until they reach the edge of my pool coping and then they eventually jump and often end up in the water.
They are not good swimmers but I have seen them manage to climb back up onto the tile if they reach the wall. If they don’t manage to get out they will climb up on whatever they can… rafts, leaves, the cleaner hose, your arm. If they don’t escape they will slowly die and either sink to the bottom or end up in the skimmer baskets. On the plus side, I have not had any issues with them clogging up my system but they definitely rattle my nerves!
One thing I did invest in is a solar powered pool skimmer robot (Solar Breeze Ariel). It’s like a Roomba for the surface of your pool. That little gem catches plenty of lanternflies! Did I mention they die slowly? So yeah that makes emptying the basket on Ariel a real challenge. I have anxiety and a wicked startle reflex so I may have screamed and thrown the debris tray a few times while attempting to empty it!

If they don’t end up inside Ariel, they climb up it for a ride because that is just what they do.
Consult the Penn State Extension, pest control, arborists and landscapers if you have questions or need advice. Back in 2018, we homeowners were learning right alongside all those people so at least more information is available now to anyone just getting hit with this horribly invasive insect. If you have any neighbors with pools, I would ask them how their experience has been. I sincerely wish you the best of luck and hope you enjoy the pool!