iPhone 15 Pro motherboard needs replacing after 13 months

Unfortunately the warranty says 1 year. After that you're responsible for any repairs unless it is one of the rare product service bulletins for a particular model. If you have AppleCare then you get a reduced cost repair, but as with any extended warranty, the vendor is the winner in the long run. It would be nice to have it in action for this (but you have to buy it in advance) but this is a rare event. We never buy AppleCare or our devices and we purchased our last iPhone with what we had saved by not buying Apple Care on all the others. It's up to you. In my opinion its mostly worth it if you really cannot afford the occasional expensive repair.

install the mobile Apple Support app and contact Apple using that. You can then optionally allow Apple technicians to have direct access to diagnostic data from your device.

Go to this page to find your nearest Apple Authorized Service Provider (AASP) or Apple Authorized Distributor (AAD) --> Find Locations

How to make a Genius Bar appointment

1. Go to Genius Bar Reservation and Apple Support Options - Apple

2. Go to "Get hardware help".

3. Select your hardware and continue selecting options requiring replacing parts until you see "Bring in for Repair"

4. Sign in with your Apple ID

or:

Refer to this document for ways to contact Apple ➞ Choose your country or region - Official Apple Support

Select your country (also look for "other" regions), then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.

or:

Contact Apple for support and service by telephone ➞ Contact Apple for support and service - Apple Support

For the iPhone Service Answer Center click here --> Choose Your Country or Region - Apple Support

Select your country.

For a cost estimate:

- Scroll down to "Get an estimate"

- Enter the service required

- Enter the iPhone model you have

- Enter the version of that model

- Click "Get estimate"

For instructions on how to get your iPhone, iPad, or iPod touch ready for service click here --> Prepare your iPhone or iPad for service - Apple Support

- "To protect your information and save time, follow these steps before you get service for your device."

When Apple make a repair they will fix all the issue they found on the device this is to ensure that when you receive the device back it is working 100%.

Since there's a damage on the back there will be a fee to have it service, unless you have coverage purchased like AppleCare+ to cover it.

They’ve advised me the motherboard needs replacing, and because I have a crack on the back as well, it will be 1k to fix.

Well, the back of the phone does not crack by itself. The phone was dropped, or in a back pocket when you sat on it.....or something similar. The point is, the phone was physically damaged and the stress on the phone likely translated to a stress on the motherboard, breaking a solder joint or connector.

but 13 months is a bit rich at that much.

It could have been 13 days, but the time is not relevant. The damage to the phone is the issue here.