How do you prepare a laptop for repair?

The "standard" way (the "safe" one) is to "clone" the hard disk (please read as make a dd-like or "forensic sound" image) then wipe the disk, install a basic OS, give it to repair, and then re-image the hard disk back.

BUT this will take anyway a few hours time (imaging a disk takes time) of which some will need to be "attended".

The fastest would be as someone else suggested, to remove phisically the disk and store it safely, but you need a replacement disk (HDD or SDD) to put in the machine, otherwise the repair service won't probably be able to fully test the machine after the repair, and of course there are many laptops where you need to open the laptop to remove and replace the hard disk, so the time would be more or less the same as replacing the battery yourself.

Depending on how you have organized your data, you may be able to more simply backup, delete (securely if needed), and then restore just the data, but if the scope is "security" it is far from foolproof, and it will take anyway some time.

I believe that this (and the issues in transferring data when/if you change laptop/PC) is one of the unresolved problems of modern computing, there is so many data (scattered almost everywhere on the disk) that the only way to be sure that nothing is lost is to image the disk and - on the other hand - there is no (that I know of) way to make sure that you backed up and deleted all the data short of wiping the disk.

A good practice is to have all application data on a separate volume/partition, different from the one to which the OS is installed, but this only covers the actual documents as almost any setting will be on the OS volume anyway.

Doesn't sound like you have the time to remove the drive, because it's about the same amount of work as a battery swap these days. I went that route last time I needed a keyboard replacement under warranty. I don't think there's much else you can do except find a trusted repair person.

You backup your laptop, bare metal with something like Veeam or at file system level using Restic, and wipe the disk.

After repair, restore.

Just dismount the HDD/SDD if no encryption. I would never buy a laptop without ability to change battery without a disassemble.