I created a script that I dropped into /etc/cron.hourly which does the following:

1. Use rsync to mirror my root partition to a btrfs partition on another hard drive (which only updates modified files).
2. Use btrfs subvolume snapshot to create a snapshot of that mirror (which only uses additional storage for modified files).
3. Moves “old” snapshots into a trash directory so I can delete them later if I want to save space.

It is as follows:

#!/usr/bin/env python
from datetime import datetime, timedelta
import os
import pathlib
import shutil
import subprocess
import sys

import portalocker

DATETIME_FORMAT = '%Y-%m-%d-%H%M'
BACKUP_DIRECTORY = pathlib.Path('/backups/internal')
MIRROR_DIRECTORY = BACKUP_DIRECTORY / 'mirror'
SNAPSHOT_DIRECTORY = BACKUP_DIRECTORY / 'snapshots'
TRASH_DIRECTORY = BACKUP_DIRECTORY / 'trash'

EXCLUDED = [
    '/backups',
    '/dev',
    '/media',
    '/lost+found',
    '/mnt',
    '/nix',
    '/proc',
    '/run',
    '/sys',
    '/tmp',
    '/var',

    '/home/*/.cache',
    '/home/*/.local/share/flatpak',
    '/home/*/.local/share/Trash',
    '/home/*/.steam',
    '/home/*/Downloads',
    '/home/*/Trash',
]

OPTIONS = [
    '-avAXH',
    '--delete',
    '--delete-excluded',
    '--numeric-ids',
    '--relative',
    '--progress',
]

def execute(command, *options):
    print('>', command, *options)
    subprocess.run((command,) + options).check_returncode()

execute(
    '/usr/bin/mount',
    '-o', 'rw,remount',
    BACKUP_DIRECTORY,
)

try:
    with portalocker.Lock(os.path.join(BACKUP_DIRECTORY,'lock')):
        execute(
            '/usr/bin/rsync',
            '/',
            MIRROR_DIRECTORY,
            *(
                OPTIONS
                +
                [f'--exclude={excluded_path}' for excluded_path in EXCLUDED]
            )
        )

        execute(
            '/usr/bin/btrfs',
            'subvolume',
            'snapshot',
            '-r',
            MIRROR_DIRECTORY,
            SNAPSHOT_DIRECTORY / datetime.now().strftime(DATETIME_FORMAT),
        )

        snapshot_datetimes = sorted(
            (
                datetime.strptime(filename, DATETIME_FORMAT)
                for filename in os.listdir(SNAPSHOT_DIRECTORY)
            ),
        )

        # Keep the last 24 hours of snapshot_datetimes
        one_day_ago = datetime.now() - timedelta(days=1)
        while snapshot_datetimes and snapshot_datetimes[-1] >= one_day_ago:
            snapshot_datetimes.pop()

        # Helper function for selecting all of the snapshot_datetimes for a given day/month
        def prune_all_with(get_metric):
            this = get_metric(snapshot_datetimes[-1])
            snapshot_datetimes.pop()
            while snapshot_datetimes and get_metric(snapshot_datetimes[-1]) == this:
                snapshot = SNAPSHOT_DIRECTORY / snapshot_datetimes[-1].strftime(DATETIME_FORMAT)
                snapshot_datetimes.pop()
                execute('/usr/bin/btrfs', 'property', 'set', '-ts', snapshot, 'ro', 'false')
                shutil.move(snapshot, TRASH_DIRECTORY)

        # Keep daily snapshot_datetimes for the last month
        last_daily_to_keep = datetime.now().date() - timedelta(days=30)
        while snapshot_datetimes and snapshot_datetimes[-1].date() >= last_daily_to_keep:
            prune_all_with(lambda x: x.date())

        # Keep weekly snapshot_datetimes for the last three month
        last_weekly_to_keep = datetime.now().date() - timedelta(days=90)
        while snapshot_datetimes and snapshot_datetimes[-1].date() >= last_weekly_to_keep:
            prune_all_with(lambda x: x.date().isocalendar().week)

        # Keep monthly snapshot_datetimes forever
        while snapshot_datetimes:
            prune_all_with(lambda x: x.date().month)
except portalocker.AlreadyLocked:
    sys.exit('Backup already in progress.')
finally:
    execute(
        '/usr/bin/mount',
        '-o', 'ro,remount',
        BACKUP_DIRECTORY,
    )