Trying to find a way to stop syncing a specific folder

First LrC Does NOT Sync Folders. It will sync one or multiple Collections. Collections ARE NOT Folders.

So please describe exactly what you are doing.

To answer your key question, "Is there a way to remove all content from everything from web to device without impacting lightroom classic?" go to All Synced Photos in Classic's Catalog panel and remove all photos from there. That's a crude way.

Alternatively, go to each Synced collection in the Collections panel, change the filter box to Synced Collections, and then unsync every collection. Once done, clear up anything left in All Synced Photos as above. This is the better way,

You should also go to Deleted Items by logging into LrWeb in a browser. Empty this, and you free up more cloud allocation.

What this does is clear everything from the cloud, including originals which are still using up space in LR on your phone. With originals now cleared from the cloud/devices, you can now resync collections and you'll get the photos back onto your devices but as "smart previews", compressed versions of the photos, using less space on devices and not using any of your allocation.

How are you taking photos on the phone? Using the LR camera or the camera's built-in one? And what type of phone?