After inputting the FileVault recovery key, MacBook just restarts and nothing else happens

What is the exact model of this Mac and version of macOS? You can get the exact model by entering the system serial number here:

Check Your Service and Support Coverage - Apple Support

Are you trying to unlock Filevault or reset a macOS user account password?

My guess is the APFS file system is damaged so the volume is unable to be mounted. I have encountered this issue several times over the years while supporting our organization's Macs. If this is the case, then you may need to try to manually mount the volume as read-only using the command line. If you are not familiar with the command line, then it would be easiest to install macOS to an external USB3 SSD so you can try working while booted from the external drive to attempt to access the data on the internal drive if you need to get a backup.

If you already have a good backup, then it will probably be easiest to just perform a clean install of macOS by first erasing the SSD followed by reinstalling macOS & restoring from backup.

Make sure when you enter the Filevault recovery key that you then actually change the macOS user account (or was that just for the Filevault) password right then & there. I just recently had to do this for one of our organization's laptops because the laptop said the account was locked, but I don't recall the specifics (we knew the password, but it would not allow us to authenticate...one of the problems with T2 models even without Filevault enabled). I know with the 2018-2020 Intel Macs with the T2 security chip, that Filevault is just further protecting the user account passwords by adding another password unlike with the older Macs (not entirely sure how it works since Apple really doesn't provide details).

If you cannot reset the password of Filevault and an admin macOS user account, then you will need to perform a clean install of macOS by erasing the whole physical SSD (Intel Macs only), or by performing a firmware "Restore" to reset the firmware & T2 security chip which wipes the internal SSD requiring reinstalling macOS through Internet Recovery Mode (only way once the internal SSD has been erased through a firmware "Restore").

Revive or restore an Intel-based Mac using Apple Configurator - Apple Support

Unless you previously modified the security settings to allow booting from USB, then you won't be able to do so now unless you can authenticate with at least one admin user account. A clean install of macOS through Recovery Mode, or a firmware "Restore" & Recovery Mode install will be required. If you can authenticate with the T2 security chip, then you can modify the Mac's security settings using the Startup Security Utility.

I hope you have a backup because there is no way to access the data on the internal SSD because it requires authentication with the T2 security chip with one of the macOS user accounts to unlock the hardware encryption of the internal SSD (the SSD is always hardware encrypted on T2 models even if Filevault is not enabled) even if trying to access it through Target Disk Mode. There are a lot more ways to lose access to data on the internal SSDs of these newer Macs due to all the hardware, software, and security changes (especially the 2018+ Macs). I've seen several bugs with T2 Macs for allowing authentication (passwords were known as I could log in when booted normally, but authentication & access from Recovery Mode or Target Disk Mode did not work).

What is the exact model of your Mac? You can get this information by entering the system serial number using this link:

Check Your Service and Support Coverage - Apple Support

The exact model is important since later model Macs have extra security features and behave differently so they change & limit some options such as booting from USB especially if you never explicitly allowed this option prior to being locked out. Generally if you have a Filevault recovery key you should be able to use it to reset one of the macOS admin user accounts' passwords.

https://support.apple.com/en-us/HT202860