Linux Mint (Ubuntu) always use a swapfile on installation, but swapfile on the main subvolume does not work on Btrfs.
To fix this, we need to create a new subvolume and put the swapfile there.

Assuming that / is on /dev/sda2 (/dev/sda1 if you are still using old BIOS, /dev/nvme0n1p2 if you are using NVME) and Linux Mint is installed at / on @ subvolume and /home is on @home subvolume.

1. Mount /dev/sda2 to /mnt.
   sudo mount /dev/sda2 /mnt
   If you run ls /mnt, you’ll see @, @home and other subvolumes that may be there.
2. Create a new @swap subvolume.
   sudo btrfs sub create /mnt/@swap
3. Unmount /dev/sda2 from /mnt.
   sudo umount /mnt
4. Create /swap directory where we plan to mount the @swap subvolume.
   sudo mkdir /swap
5. Mount the @swap subvolume to /swap.
   sudo mount -o subvol=@swap /dev/sda2 /swap
6. Create the swap file.
   sudo touch /swap/swapfile
7. Set 600 permissions to the file.
   sudo chmod 600 /swap/swapfile
8. Disable copy-on-write for this file.
   sudo chattr +C /swap/swapfile
9. Set size of the swap file to 4 GB as an example.
   sudo fallocate -l 4G /swap/swapfile
10. Format the swapfile.
    sudo mkswap /swap/swapfile
11. Turn the swap file on.
    sudo swapon /swap/swapfile
    Now the new swap should be working.
12. Type sudo xed /etc/fstab to open fstab in text editor. Be careful with this file as it can easily cause your system not to boot.
13. Remove /swap/swapfile none swap sw 0 0 at the last part.
14. Add these lines at the last part of fstab:

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UUID=XXXXXXXXXXXXXXX /swap btrfs subvol=@swap 0 0
/swap/swapfile none swap sw 0 0

Use the UUID of your /dev/sda2. Save the file.

15. Remove the old swapfile created by the installer. sudo rm -f /swapfile

Note: If your CPU is fast enough for zRAM, use zRAM instead.

Sources:\

1. Can I have a swapfile on btrfs?
2. Can I have a swapfile on btrfs?