Drupal core dependency error when updating to 2.1.0

drupal/barcodes 2.1.0 requires tecnickcom/tc-lib-barcode ^2.0
This is true.
drupal/recommended-project - requires tecnickcom/tc-lib-barcode (^1)
Where is this requirement coming from?

I have Barcodes 2.1.x installed on a Drupal 10.3 sites, so I know it works.

I tried this on a clean 10.3 site:

$ composer create-project drupal/recommended-project:^10.3 test-10-3
$ cd test-10-3/
$ composer require drupal/barcodes:2.0.7

This worked, installed Barcoded 2.0.7

  - Locking drupal/barcodes (2.0.7)
  - Locking tecnickcom/tc-lib-barcode (1.18.4)
  - Locking tecnickcom/tc-lib-color (1.14.39)

Then I tried:
$ composer require drupal/barcodes:^2.1
This failed, with the same error you showed.
Then I tried:
$ composer require drupal/barcodes:^2.1 -W
This worked - this upgraded the tecnickcom/tc-lib-barcode library at the same time as it upgraded drupal/barcodes:

  - Upgrading drupal/barcodes (2.0.7 => 2.1.0)
  - Upgrading tecnickcom/tc-lib-barcode (1.18.4 => 2.3.1)
  - Upgrading tecnickcom/tc-lib-color (1.14.39 => 2.2.3)

So I'm not sure why you are having a problem, unless you have something else installed that requires tecnickcom/tc-lib-barcode :^1

If you leave off the -W, then it will fail like you observed, but when you tell composer to update with the dependencies then it really should be updating tecnickcom/tc-lib-barcode at the same time.

Thanks for your help. I finally find the problem. A very old manual edition of my composer.json

It works with Drupal 10.3.5