You are in luck, the Shure SE425's use an MMCX connector on the buds, so there are a zillion 3rd party cables available - or complain to Shure and ask them to send a replacement cable to try to see if that fixes it.
I haven't had any 3.5mm compatibility issues with any connectors so far, but in the past I have had some incompatible connectors - the width of the bands is just a bit off - and the device acts like you are describing.
Looks like a nice headset, and Shure is having a sale right now on both the wireless and wired models - they are both $199 right now, and the wireless model comes with both wired and wireless harnesses with MMCX connectors, so you could try getting a set of the wireless to get the best of both options. I usually get 2 or even 3 of the same unit if I really like it to rotate usage to help them last longer, and as they age out and sell out you can usually get great deals on them as they are discontinued.
If you don't need the microphone or controls - I usually get 3rd party cables without the microphone / control pod - there are a lot of "upgrades" for cables that are inexpensive these days, here's a thread about them here on head-fi:
https://www.head-fi.org/threads/low-end-cheap-generic-otherwise-bang-for-buck-cable-thread.891911/
I've settled into using the KB EAR 8 core and 16 core models, but there are lots of other brands and choices:
https://www.amazon.com/s?k=8+core+mmcx+cable
https://www.amazon.com/s?k=16+core+mmcx+cable
And, as long as you are considering replacing the cable, I'd try a balanced cable - the BTR5 puts out more power on the 2.5mm balanced connector:
https://www.amazon.com/Detachable-Upgrade-Earphone-Replacement-Standard/dp/B07ZCR2FVR
https://www.amazon.com/Silver-Plated-Braided-Upgrade-Earphone/dp/B07V1TW79V/
Depending on the headphone and your own hearing sensitivities you might like cable upgrades with Copper only wire strands, Copper with silver plating, or a mix of the two. Bright headphones can benefit from copper only, bass heavy dark sounding headphones can benefit from silver plating, and a combination of the two is good for balanced headphones that just need a cable upgrade.
Please come back and let us know what you end up trying and what you find works best for you and those Sure SE425's