Re:" I recently encountered an issue with an accidental subscription that resulted in a $45 charge to my account".
We are all Apple users, like yourself, in the community, so we have no access to your accounts or details.
It seems that free trials need to be cancelled at least 24 hours before they expire, if you do not want to be charged.
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Re:" I contacted Apple Support to request a refund, explaining that I did not intend to subscribe and have not used the service at all. Unfortunately, my request was denied,
Am no expert in this area, just an Apple user, like yourself.
Below is my understanding of some of the procedures in place:
Apple provides an article. about how to request a refund ...ie: if money has been deducted (not pending) by Apple.
You can: Request a refund for apps or content that you bought from Apple - Apple Support
A request that was made and was denied could mean that the subscription was not to one of Apple's own products, and therefore Apple does not have your money. The money could be in the hands of the subscription's developer or the vendor / supplier who provides access to the subscription.
The subscription is likely available to you, and charges may continue, whether you have used it or not, unless you have cancelled it. If needed: See what to do: If you want to cancel a subscription from Apple - Apple Support
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Re: "... and I’m now looking for guidance on how to navigate this situation."
The best source of help for a product not made by Apple (a third-party product) is the company or person who made it—its vendor or developer: See how to: Contact a third-party vendor - Apple Support
or
How to contact an app developer - Apple Support
If needed: Apple has a "Report a problem" web-page: https://reportaproblem.apple.com/?s=6
All the best :-)