Is it considered a bad practice to store key and encrypted files next
to each other?
Yes, not ideal to put the key in the same place as the cipher text. For example, perhaps files on the open LUKS containers are archived and uploaded to the same object storage account, as a file based backup. An adversary paying attention will take the private key and attempt to decrypt with it.
A separate LUKS volume may be more secure to the extent that it makes the plain text less accessible. Only opening the volume for as long as you do GPG operations lessens the exposure.
In the real world, practical compromises are necessary. On disk keys are easy to use. Passphrase protected key slows an attacker from using it, but its only a matter of time. If a copy of a GPG private key is taken, consider it compromised. Consider rekeying.
Are there any alternatives to that dilemma?
Ideally, do not store the private key on an online storage. Use a smartcard hardware token for private key, YubiKey or similar. Store cold backups on tiny storage devices or paper keys, and put these a secure offline place, like the business continuity safe. Extraordinary measures, but secrets are special as they unlock other data.