Is replacing a defective product and refunding its price, instead of repairing it according to the owner's desire, considered a breach of trust or forbidden by Islamic law?

What the questioner did falls under the category of an unauthorized agent's ( فضولي ) action, which is a matter of scholarly disagreement regarding its validity and religious ruling. The buying and selling by an unauthorized agent is valid but, according to the well-known opinion, it is prohibited and non-binding; its binding nature depends on the owner's consent. The Malikis hold that an unauthorized agent's sale without a benefit for the owner is forbidden, but if he sells for a benefit, such as fearing damage, then it is not forbidden; rather, it might even be recommended. It appears that the unauthorized agent's action does not entail sin for the doer if his intention was the owner's benefit and he presumed his consent. The questioner does not sin if his action was for the benefit of its owner, but it is better to inform the owner and seek permission before acting.