Transaction Log backup in MSSQL's HADR
Can I use my DR node as a &quot;backup&quot; in case something went wrong instead of restoring my database using our last daily backup and then procedurally restore the entire transaction log backup from that day?

No.  All changes, including ones you might like to undo, are automatically written to your AG secondaries.  You should take log backups on exactly one replica and all the backups should go to a single location.  You can configure a Backup Preference to help make sure that 1) backups are being taken, and 2) they are taken on your preferred node if it is available.