Backup external drive size needed.

According to the Time Machine support article.

• Use a storage device with at least twice the storage capacity of your Mac. For example, if your Mac has 1TB of storage, your backup disk should ideally have at least 2TB of storage. If Time Machine needs more storage space, your Mac will let you know.
• Use your Time Machine backup disk only for Time Machine backups, not for storage of other files.*

For reference see > Back up your Mac with Time Machine - Apple Support

Note: If you have file's or media libraries stored on an external drive to save space on your internal drive..?

Then you may need a 3 or 4T backup drive to backup both your internal and external drives.

pslb wrote:

I have a 2021 16GB Mac I want to back up with Time Machine to transfer to my new Mac. The 1TB LaCie drive tells me it is too small for the job. Really? Thank you.

Officially, Apple suggests double the capacity, minimally.

Local preference is roughly 2.5 to 3 times the size of internal main storage, or larger.

That 1 TB LaCie storage device would be suitable for a hypothetical 256 GB internal storage configuration, but (locally) would be borderline insufficient for a 512 GB configuration.

That this storage is larger than internal storage allows additional copies of actively-modified files to be saved; deeper backups. This is handy if the last few copies of a file are somehow corrupt, or if a whole series of changes need to be backed out.

Time Machine does not react particularly well to big files getting churned, hence higher local practices.

You should size your TM drive to be about 2x what is used on the Mac. In other words just because you have a 1TB internal drive but are only using 500GB ever then your TM drive would work fine at 1TB or larger.