Is it worth to repair my 2013 MacBook pro with retinal display?

+1 on Bob's sage advice. I think you have the perfect storm of issues and there are numbers to support that.

• A new battery for a Retina MBP installed by Apple is US$200. It is not done in-store any more so Apple will have to ship it to a specialized repair/refurb facility. Figure a week to 10 days.
• If you have a independent service person do the battery, expect it to be closer to $500.
• Same $500 if the swelling battery bent the upper deck, but that includes a battery.
• A cracked Retina screen requres the entire display unit to be repalced. Usual cost: betwen $500 and $650 depending on screen size.
• The swelling battery, in addition to potentially ruining the upper deck, could have damaged the logic board. Not sure about the current price but a few years back, an LB change-out was betwen $700 and $1100.

Easy decision for me. A new 13-inch MBP M1 with an optional 512GB SSD is US$1500. Worst case is that the repairs could cost more than that.

Allan Jones wrote:

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Easy decision for me. A new 13-inch MBP M1 with an optional 512GB SSD is US$1500. Worst case is that the repairs could cost more than that.

Or potentially yet cheaper, as this Mac is being used as a desktop and not as a laptop, which means a Mac mini at USD$1100 for 16 GB with 512 GB SSD (plus monitor), or an iMac 21.5” 16 GB 1 TB fusion for USD$1300, or a bigger iMac, is potentially in play.

I’ve run purchasing and pricing configurations for folks where a nice iMac and a nice iPad is cheaper than a nice MacBook Pro, too.

And as the two replies have already suggested, I too would replace this with a newer or new, and not repair. Not repairing a MacBook Pro that either can’t run the current macOS software (early 2013), or that is the oldest MacBook Pro (late 2013) that can run current macOS software.

Personally I would not spend any money on an obsolete/vintage computer.

Obtaining service for your Apple product after an expired warranty - Apple Support