Case by case. Depends on parts availability. Go onto Apple's website and book for a service slot. Apple may arrange with you a remote diagnostic check first. One thing to note, always go to Apple Store, never ever go to an Authorised Apple Service Centre.

I was told that for this model, they need to swap the entire keyboard, track pad, in order to replace the battery.

They need to swap out the top case assembly and this consists of the case itself, the keyboard, track pad and battery.

Can the repair be done in the same day, or does it typically take several business days?

Technically speaking, the repair "can" be done in a day. In fact, it's a very simple repair and takes approximately 30 mins from start to completion. However, the total process can take up to a week or more depending on where you are in the repair queue and parts availability. If it takes more than a day, you can bet it is because they don't have the parts available.

It's important to remember, Apple Stores are set up to sell new products - they are not a repair facility. There are only a couple/three technicians that are actually qualified (by Apple) to do the repair. They are usually inundated with iPhone/iPad repairs mostly, then computer repairs. Having technician and parts availability is a complex process and (IMO) this is not Apple's wheelhouse.

They do not offer loaners. This is why I'm a strong proponent of having a backup strategy that goes beyond Time Machine; you back up your data in multiple places so if you're without a Mac for an extended period, you can continue to work even if the temporary machine isn't Apple.

In 2022 this depends. Many batteries are glued to the top case, so the batteries may or may not be swapped locally or sent out to a repair center with larger staff and parts warehoused outside the retail store.

When this question was asked, it was nearly 100% yes - all computer batteries from Apple (including the newer unibody models where the battery is not consumer replaceable) are easily swapped in a 10 to 35 minute procedure to open, inspect, replace, test and document the repair. This assumes the technician has all the parts, adhesives, solvents in place and has done a dozen or so of this exact model so they only have to refresh the steps and not have to carefully study the manual and find each screw and piece to remove.

Of course, your wait time might be longer if no one is free to start work immediately or the part needs to be retrieved from a nearby stock room. If the part isn't in stock, Apple should be able to quote you a delivery time to order the part, and discuss if you want to leave the Mac for service, choose mail in service or leave with your mac and return later to get the repair done as same- or next-day service once the part and the Mac are in the shop together.

Since you called AppleCare and explained your symptoms, my guess is they cannot run the diagnostics remotely to establish a true failure (or if you agree to pay for the repair) and pre-order the part before you present the Mac for repair in the store.

My experience is each store has sufficient stock to do several repairs of a battery type, but that being said, I've also gone in on a busy day where they had three machines needing the same part as I and I was the third in line and therefore had the option of leaving the Mac or waiting for the part to arrive.

Worst case, you get a diagnosis and don't leave the machine in for repair, but have options to pre-order the part when you return or find another store. If the store mails in your Mac for repair, often it can get overnighted to a return location of your choosing and clearly wherever they ship the machine will be same day service for an in-stock battery at the main repair depot.

Since a few years before Covid, I’ve personally been all in on arranging service for everything online first and having a box shipped to my house / business even with multiple retail stores within 25 minute drive. Staffing online and remote diagnosis replace much of what I needed to get in person previously. The iPad and iOS app is easiest for me, even arranging Mac repairs.

If they have it in stock, it doesn't take long. If they don't, essentially what they do it give you a virtual place in line among customers at that store. They'll contact you when they have one for you and you have many 3 days to make a drop-in visit for the installation. There are reports that some people are being told it's taking longer at some stores than others. I suspect that the allocations of batteries are based on location, but it would be difficult to know where to go where you might get it earlier.

You're not the only one who needs a battery replacement. They are probably waiting on supplies before they can do the repair. The entitlement is what's insane here. 3-5 days is nothing.