3TB Airport Time Capsule full, no longer backing up

The LaCie hard drive can be connected to the USB port on the AirPort Time Capsule, so you can back up your Mac(s) to that drive by selecting the hard drive as a target for Time Machine backups.

When you do that, Time Machine will start all over again with a new full complete backup of your Mac(s) on the LaCie drive, then continue incremental backups on the LaCie drive.

Since the Time Capsule is full, you would remove the Time Capsule as a target for Time Machine backups. After a few months, you may likely find that you really don't need all the old backups on the Time Capsule that go back weeks, months and even years into the past......(few of us ever do). At that point, you can erase the Time Capsule drive and use it as a spare hard drive.

The USB port on the Time Capsule is an older USB 2.0 design, so while it will work for Time Machine backups, you will likely notice that backups in general take longer than they did when they went directly to the Time Capsule hard drive.

Glad that your Time Capsule has been working well, but would also point out that 5 years is about the time on average, that the product starts to become "suspect", so it would not be a good idea to keep data stored on the Time Capsule that you cannot afford to lose.

You can’t “extend” it, but you can move a Time Machine backup from one disk to another, then use the new larger disk to continue your Time Machine backups.

https://support.apple.com/en-us/HT202380

Sorry, but no. There is no method available that will allow you to "extend" the storage capacity for Time Machine backups, and that is primarily due to the way TM creates and uses these backup sets.