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Simply put, is there a way to destroy items in the inventory instead of consuming them (e.g. parchments or messages you don't need anymore), breaking mugs, etc.?

Of course, it is best to account for realism here as we cannot destroy swords, armor and the like with our bare hands. These might bring a message saying "you can't destroy this item".

Initially triggered by a personal desire to rip unnecessary or draft parchments (if we can delete written messages on parchments that will be great as well), I am open to alternative options.

why do you want destroy if you can sell the stuff ?

You can burn parchment at wall torches and standing lamps I believe.

Just hold it in your hand and activate the torch, or click the parchment, I don't remember which.

Or sell them at the Hemp NPC

Each town has a donation bin that can essentially work as a trash bin for most items. This also helps monthly gem output.

Torches/oil lamps/lanterns/candles both static and ones you hold in your hand can be used to burn parchments. As Jojee said, though not limited to just the wall torches and standing lamps. Activated by having a parchment in hand when clicking one of the lit items.

Items can also of course be sold as mentioned by Yridia.

A select few items you'll just have to leave on the ground to rot naturally, disappearing after 22ish hours I think it was, as the donation bin won't accept them and/or they can't be sold.

Thanks for all of your guidance and suggestions. These will do nicely.