So, I tried to install Klarna Checkout on my Magento 2.3 instance via the Web Setup Wizard and ran into the same problem that you had (except my output showed the problem for some reason).
We found conflicting component dependencies. Hide detail
Command "update" failed: Loading composer repositories with package information
Updating dependencies (including require-dev)
Your requirements could not be resolved to an installable set of packages.
Problem 1
- klarna/module-core 3.0.0 requires magento/module-payment 100.0.0 - 100.0.12 || 100.1.0 - 100.1.7 || 100.2.0 -> satisfiable by magento/module-payment[100.0.2, 100.0.3, 100.0.4, 100.0.5, 100.0.6, 100.1.0, 100.1.1, 100.0.7, 100.1.2, 100.1.3, 100.0.8, 100.1.4, 100.0.9, 100.1.5, 100.0.10, 100.0.11, 100.1.6, 100.1.7, 100.0.12, 100.2.0].
- klarna/module-core 3.1.0 requires magento/module-payment 100.0.0 - 100.0.12 || 100.1.0 - 100.1.7 || 100.2.0 -> satisfiable by magento/module-payment[100.0.2, 100.0.3, 100.0.4, 100.0.5, 100.0.6, 100.1.0, 100.1.1, 100.0.7, 100.1.2, 100.1.3, 100.0.8, 100.1.4, 100.0.9, 100.1.5, 100.0.10, 100.0.11, 100.1.6, 100.1.7, 100.0.12, 100.2.0].
- klarna/module-core 3.1.1 requires magento/module-payment 100.0.0 - 100.0.12 || 100.1.0 - 100.1.8 || 100.2.0 - 100.2.1 -> satisfiable by magento/module-payment[100.0.2, 100.0.3, 100.0.4, 100.0.5, 100.0.6, 100.1.0, 100.1.1, 100.0.7, 100.1.2, 100.1.3, 100.0.8, 100.1.4, 100.0.9, 100.1.5, 100.0.10, 100.0.11, 100.1.6, 100.1.7, 100.0.12, 100.2.0, 100.1.8, 100.2.1].
- klarna/module-core 3.2.2 requires magento/module-payment 100.0.0 - 100.0.12 || 100.1.0 - 100.1.8 || 100.2.0 - 100.2.1 -> satisfiable by magento/module-payment[100.0.2, 100.0.3, 100.0.4, 100.0.5, 100.0.6, 100.1.0, 100.1.1, 100.0.7, 100.1.2, 100.1.3, 100.0.8, 100.1.4, 100.0.9, 100.1.5, 100.0.10, 100.0.11, 100.1.6, 100.1.7, 100.0.12, 100.2.0, 100.1.8, 100.2.1].
- klarna/module-core 3.2.3 requires magento/module-payment 100.0.0 - 100.0.12 || 100.1.0 - 100.1.8 || 100.2.0 - 100.2.1 -> satisfiable by magento/module-payment[100.0.2, 100.0.3, 100.0.4, 100.0.5, 100.0.6, 100.1.0, 100.1.1, 100.0.7, 100.1.2, 100.1.3, 100.0.8, 100.1.4, 100.0.9, 100.1.5, 100.0.10, 100.0.11, 100.1.6, 100.1.7, 100.0.12, 100.2.0, 100.1.8, 100.2.1].
- klarna/module-core 3.2.4 requires magento/module-payment 100.0.0 - 100.0.12 || 100.1.0 - 100.1.8 || 100.2.0 - 100.2.1 -> satisfiable by magento/module-payment[100.0.2, 100.0.3, 100.0.4, 100.0.5, 100.0.6, 100.1.0, 100.1.1, 100.0.7, 100.1.2, 100.1.3, 100.0.8, 100.1.4, 100.0.9, 100.1.5, 100.0.10, 100.0.11, 100.1.6, 100.1.7, 100.0.12, 100.2.0, 100.1.8, 100.2.1].
- klarna/module-core 3.2.5 requires magento/module-payment 100.0.0 - 100.0.12 || 100.1.0 - 100.1.8 || 100.2.0 - 100.2.1 -> satisfiable by magento/module-payment[100.0.2, 100.0.3, 100.0.4, 100.0.5, 100.0.6, 100.1.0, 100.1.1, 100.0.7, 100.1.2, 100.1.3, 100.0.8, 100.1.4, 100.0.9, 100.1.5, 100.0.10, 100.0.11, 100.1.6, 100.1.7, 100.0.12, 100.2.0, 100.1.8, 100.2.1].
- klarna/module-ordermanagement 4.1.3 requires php ^5.6|~7.0.13|~7.1.0 -> your PHP version (7.2.13) does not satisfy that requirement.
- klarna/module-ordermanagement 4.1.2 requires php ^5.6|~7.0.13|~7.1.0 -> your PHP version (7.2.13) does not satisfy that requirement.
- klarna/module-ordermanagement 4.1.0 requires php ^5.6|~7.0.13|~7.1.0 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.2.1 requires php 7.0.2|7.0.4|~7.0.6|~7.1.0 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.1.8 requires php ~5.6.5|7.0.2|7.0.4|~7.0.6 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.2.0 requires php 7.0.2|7.0.4|~7.0.6|~7.1.0 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.0.12 requires php ~5.5.0|~5.6.0|~7.0.0 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.1.7 requires php ~5.6.5|7.0.2|7.0.4|~7.0.6 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.1.6 requires php ~5.6.5|7.0.2|7.0.4|~7.0.6 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.0.11 requires php ~5.5.0|~5.6.0|~7.0.0 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.0.10 requires php ~5.5.0|~5.6.0|~7.0.0 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.1.5 requires php ~5.6.5|7.0.2|7.0.4|~7.0.6 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.0.9 requires php ~5.5.0|~5.6.0|~7.0.0 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.1.4 requires php ~5.6.5|7.0.2|7.0.4|~7.0.6 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.0.8 requires php ~5.5.0|~5.6.0|~7.0.0 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.1.3 requires php ~5.6.5|7.0.2|7.0.4|~7.0.6 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.1.2 requires php ~5.6.5|7.0.2|7.0.4|~7.0.6 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.0.7 requires php ~5.5.0|~5.6.0|~7.0.0 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.1.1 requires php ~5.6.0|7.0.2|~7.0.6 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.1.0 requires php ~5.6.0|7.0.2|~7.0.6 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.0.6 requires php ~5.5.0|~5.6.0|~7.0.0 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.0.5 requires php ~5.5.0|~5.6.0|~7.0.0 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.0.4 requires php ~5.5.0|~5.6.0|~7.0.0 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.0.3 requires php ~5.5.0|~5.6.0|~7.0.0 -> your PHP version (7.2.13) does not satisfy that requirement.
- magento/module-payment 100.0.2 requires php ~5.5.0|~5.6.0|~7.0.0 -> your PHP version (7.2.13) does not satisfy that requirement.
- klarna/module-om 3.0.7 requires klarna/module-core ^3.0 -> satisfiable by klarna/module-core[3.0.0, 3.1.0, 3.1.1, 3.2.2, 3.2.3, 3.2.4, 3.2.5].
- Installation request for klarna/module-om 3.0.7 -> satisfiable by klarna/module-ordermanagement[4.1.0, 4.1.2, 4.1.3], klarna/module-om[3.0.7].
Judging by the output, it’s clear that there’s an issue with PHP compatibility. This suggests that it’s trying to install something that’s not compatible with the Magento 2.3 environment.
Composer Method
So, I tried doing it via Composer (which is the way I’d usually do it). I did this by running the following command as the magento
user from the Magento root directory:
composer require klarna/m2-checkout:7.0.0
And as you can see, everything installed correctly with no errors
./composer.json has been updated
Loading composer repositories with package information
Updating dependencies (including require-dev)
Package operations: 8 installs, 0 updates, 0 removals
- Installing klarna/module-kco-core (6.0.0): Downloading (100%)
- Installing klarna/module-kco-ordermanagement (6.0.0): Downloading (100%)
- Installing klarna/module-kco (7.0.0): Downloading (100%)
- Installing klarna/checkout (v4.0.0): Downloading (100%)
- Installing phpxmlrpc/phpxmlrpc (4.3.1): Downloading (100%)
- Installing klarna/php-xmlrpc (v5.0.0): Downloading (100%)
- Installing klarna/module-kred (6.0.0): Downloading (100%)
Package phpunit/phpunit-mock-objects is abandoned, you should avoid using it. No replacement was suggested.
Writing lock file
Generating autoload files
Further Investigation
After the module installed correctly via Composer, I compared the modules that were installed against the modules that were showing available in the Web Setup Wizard. And it appears that the Web Setup Wizard allows you to install both the 2.2 and 2.3 compatible versions at the same time - Which was causing the issue.
Now knowing this, I wanted to see if I could install Klarna Checkout via the Web Setup Wizard by only selecting the modules I know I needed.

And I can confirm that omitting incompatible modules let me install Klarna Checkout without any issues.

Conclusion
The issues you seem to have faced so far are nothing you have done wrong. It’s just poor implementation by Klarna. Give it a go and let me know how you get on.