Sleep battery drain on MacOS Mojave 2015 Macbook air

Check the battery status. A five-year old battery is in need of replacing.

A Troubleshooting Procedure that may Fix Problems with macOS El Capitan or Later

You should try each, one at a time, then test to see if the problem is fixed before going on to the next.

    If possible, backup your files before proceeding.

1. Shutdown the computer and disconnect all third-party peripherals.
2. Wait 30 seconds before you restart the computer.
3. Resetting your Mac's PRAM and NVRAM
4. Reset the System Management Controller (SMC)
5. Reset your Startup Disk and Sound preferences, if needed, after resetting the PRAM.
6. Test in safe mode to see if the problem persists, then restart normally. See How  to  use  safe  mode  on  your  Mac.
7. Repair the disk by booting from the Recovery HD. Immediately after the chime hold down the Command and R keys until the Utility Menu appears. Choose Disk Utility and click on the Continue button. Select the indented (usually, Macintosh HD) volume entry from the side list.  Click on the First Aid button in the toolbar. Wait for the Done button to appear. Quit Disk Utility and return to the Utility Menu. Restart the computer from the Apple Menu.
8. Create a New User Account Open Users & Groups preferences. Click on the lock icon and enter your Admin password when prompted. On the left under Current User click on the Add [+] button under Login Options. Setup a new Admin user account. Upon completion log out of your current account then log into the new account. If your problems cease, then consider switching to the new account and transferring your files to it - Transferring files from one User Account to another.
9. Reinstall a Combo Updater  macOS  Catalina  10.15.7  Combo  Update, macOS Mojave 10.14.6 Combo Update, macOS High Sierra 10.13.6 Combo Update, macOOS 10.12.6 Combo Update, OS X El Capitan 10.11.6 Combo Update.
10. Reinstall OS X by booting from the Recovery HD using the Command and R keys. When the Utility Menu appears select Install OS X then click on the Continue button.
11. Erase and Install OS X Restart the computer. Immediately after the chime hold down the Command and R keys until the Apple logo appears. When the Utility Menu appears:

     1. Select Disk Utility from the Utility Menu and click on the Continue button.

     2. When Disk Utility loads select the drive (out-dented entry) from the Device list.

     3. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.

     4. Set the Format type to APFS (for SSDs only) or Mac OS Extended (Journaled.)

     5. Click on the Apply button, then wait for the Done button to activate and click on it.

     6. Quit Disk Utility and return to the Utility Menu.

     7. Select Install OS X and click on the Continue button.

I don't think you quite understand how Time Machine® works. It is an accumulating backup that does not delete the old files, but saves both new and old versions of files as long as they are not deleted from the Source disk. Any sized drive will eventually be filled depending on the time in use. Time Machine® is backing up, hourly.

Although your battery has only 300 or so cycles, it is also five years old (assuming you've never replaced it.) You are near the normal end of the battery's life, after five years of usage.

OK. Much easier when explained well. You should erase that backup drive, then start your Time Machine® backup from scratch. If the problem persists, then you may have a system installation problem. What you describe should not happen under normal conditions.

You should consider a faulty upgrade from High Sierra to Mojave. I don't know how you went about the upgrade, but you should consider giving it another try or at least work through my list of items as far as you can. This includes downloading and installing the Mojave Combo Updater, which may fix the problem.