Drupal 10 version upgrade Failed.

Can we start by knowing what you have already done? That file has been modified from Drupal 9. Did you truncate the error output?

My site was in Drupal version 9.5.8. and from that, tried to upgrade the version to latest Drupal 10 version.
Before ran composer update command, I'm upgraded all sub modules. Now it's support both D9 and D10.
Then uninstalled upgrade_status module and removed it from composer.json file. Next, I deleted composer.lock file and vendor folder.Then tried to run the composer update command.

First got some another errors ie,

composer update
> DrupalProject\composer\ScriptHandler::checkComposerVersion
Loading composer repositories with package information
Info from https://repo.packagist.org: #StandWithUkraine
Updating dependencies
Your requirements could not be resolved to an installable set of packages.

  Problem 1
    - zendframework/zend-feed[dev-master, dev-develop, 2.11.0, ..., 2.13.x-dev] require php ^5.6 || ^7.0 -> your php version (8.1.6) does not satisfy that requirement.
    - laminas/laminas-feed[2.12.0, ..., 2.12.x-dev] require php ^5.6 || ^7.0 -> your php version (8.1.6) does not satisfy that requirement.
    - symfony/psr-http-message-bridge[v1.1.0, ..., 1.1.x-dev] require php ^5.3.3 || ^7.0 -> your php version (8.1.6) does not satisfy that requirement.
    - symfony-cmf/routing[1.4.0-RC1, ..., 1.4.x-dev] require php ^5.3.9|^7.0 -> your php version (8.1.6) does not satisfy that requirement.
    - symfony/psr-http-message-bridge[v1.2.0, ..., v1.3.0] require php ^7.1 -> your php version (8.1.6) does not satisfy that requirement.
    - drupal/core[8.9.11, ..., 8.9.x-dev] require php ^7.0.8 -> your php version (8.1.6) does not satisfy that requirement.
    - drupal/core[9.0.10, ..., 9.0.x-dev] require php ^7.3 -> your php version (8.1.6) does not satisfy that requirement.
    - laminas/laminas-feed[2.13.0, ..., 2.14.x-dev] require php ^7.3 || ~8.0.0 -> your php version (8.1.6) does not satisfy that requirement.
    - Root composer.json requires drupal/bartik ^1.0 -> satisfiable by drupal/bartik[1.0.0-alpha1, 1.0.0, 1.0.1, 1.0.2].
    - drupal/core-recommended 10.1.0-beta1 requires drupal/core 10.1.0-beta1 -> satisfiable by drupal/core[10.1.0-beta1].
    - Conclusion: don't install drupal/core 10.1.0-beta1 (conflict analysis result)
    - drupal/core-recommended 10.1.0-rc1 requires drupal/core 10.1.0-rc1 -> satisfiable by drupal/core[10.1.0-rc1].
    - Conclusion: don't install drupal/core 10.1.0-rc1 (conflict analysis result)
    - drupal/core-recommended 10.1.0 requires drupal/core 10.1.0 -> satisfiable by drupal/core[10.1.0].
    - Conclusion: don't install drupal/core 10.1.0 (conflict analysis result)
    - drupal/core-recommended 10.1.1 requires drupal/core 10.1.1 -> satisfiable by drupal/core[10.1.1].
    - Conclusion: don't install drupal/core 10.1.1 (conflict analysis result)
    - drupal/core-recommended 10.1.2 requires drupal/core 10.1.2 -> satisfiable by drupal/core[10.1.2].
    - Conclusion: don't install drupal/core 10.1.2 (conflict analysis result)
    - drupal/core-recommended 10.1.3 requires drupal/core 10.1.3 -> satisfiable by drupal/core[10.1.3].
    - Conclusion: don't install drupal/core 10.1.3 (conflict analysis result)
    - drupal/core-recommended 10.1.4 requires drupal/core 10.1.4 -> satisfiable by drupal/core[10.1.4].
    - Conclusion: don't install drupal/core 10.1.4 (conflict analysis result)
    - Only one of these can be installed: drupal/core[8.0.0-beta12, ..., 8.9.x-dev, 9.0.0-alpha1, ..., 9.4.3, 10.0.0-alpha1, ..., 10.0.0-alpha6], drupal/bartik[1.0.0-alpha1, 1.0.0, 1.0.1, 1.0.2]. drupal/core replaces drupal/bartik and thus cannot coexist with it.
    - drupal/core[8.7.0-alpha1, ..., 8.7.7] require symfony-cmf/routing ^1.4 -> satisfiable by symfony-cmf/routing[1.4.0-RC1, ..., 1.4.x-dev].
    - drupal/core[9.0.0-alpha1, ..., 9.0.0-alpha2] require symfony/psr-http-message-bridge ^1.2.0 -> satisfiable by symfony/psr-http-message-bridge[v1.2.0, v1.3.0].
    - drupal/core[8.7.8, ..., 8.9.10] require symfony/psr-http-message-bridge ^1.1.2 -> satisfiable by symfony/psr-http-message-bridge[v1.1.2, 1.1.x-dev, v1.2.0, v1.3.0].
    - drupal/core[8.8.0-alpha1, ..., 8.8.x-dev] require zendframework/zend-feed ^2.12 -> satisfiable by laminas/laminas-feed[2.12.0, ..., 2.22.x-dev], zendframework/zend-feed[2.12.0, 2.12.x-dev, 2.13.x-dev].
    - Root composer.json requires drupal/migrate_process_inline_images ^1.0 -> satisfiable by drupal/migrate_process_inline_images[1.0.0, 1.x-dev].
    - drupal/core-recommended 10.1.0-alpha1 requires drupal/core 10.1.0-alpha1 -> satisfiable by drupal/core[10.1.0-alpha1].
    - Conclusion: don't install drupal/core 10.1.0-alpha1 (conflict analysis result)
    - drupal/migrate_process_inline_images[1.0.0, ..., 1.x-dev] require drupal/core ^8.7 || ^9 -> satisfiable by drupal/core[8.7.0-alpha1, ..., 8.9.x-dev, 9.0.0-alpha1, ..., 9.5.x-dev].
    - You can only install one version of a package, so only one of these can be installed: drupal/core[8.0.0-beta6, ..., 8.9.x-dev, 9.0.0-alpha1, ..., 9.5.x-dev, 10.0.0-alpha1, ..., 10.1.x-dev, 11.x-dev].
    - You can only install one version of a package, so only one of these can be installed: drupal/core[8.7.0-alpha1, ..., 8.9.x-dev, 9.0.0-alpha1, ..., 9.5.x-dev, 10.0.0-alpha1, ..., 10.1.x-dev, 11.x-dev].
    - drupal/core-recommended 10.1.x-dev requires drupal/core 10.1.x-dev -> satisfiable by drupal/core[10.1.x-dev].
    - Root composer.json requires drupal/core-recommended ^10.1 -> satisfiable by drupal/core-recommended[10.1.0-alpha1, ..., 10.1.x-dev].

tried to fix these error by adding some extra changes in my composer file.ie, added below lines

"symfony-cmf/routing": "^2.3",
"symfony/psr-http-message-bridge": "^6.4.x-dev",
"laminas/laminas-feed": "^2.18.2" 

and modify below lines from

"php": ">=5.6",
"composer/installers": "^1.9",  

to

"php": "^8.1",
"composer/installers": "^2.0", 

and tried to fix the errors. But it lead to these errors and not truncate the error output.

You should start with:

Only one of these can be installed: drupal/core[8.0.0-beta12, ..., 8.9.x-dev, 9.0.0-alpha1, ..., 9.4.3, 10.0.0-alpha1, ..., 10.0.0-alpha6], drupal/bartik[1.0.0-alpha1, 1.0.0, 1.0.1, 1.0.2]. drupal/core replaces drupal/bartik and thus cannot coexist with it.

#5 Removed drupal/bartik from composer.json file and added drupal/core. After running composer update command, Drupal version upgraded to version 10.1.4.
Thank you very much for your support!

You should usually not have drupal/core explicitly in composer.json. I know for fact it leads to support requests. The recommended-project template does not: https://github.com/drupal/recommended-project/blob/10.1.x/composer.json