The target setting in Core updaters points the module to which PHP version of the core files you want to update next, not what version you're currently running on your server at the moment. This is VERY useful you are debugging modules errors moving forward with PHP and you need to roll back to php7.4. You should always set this to 'Server PHP version' if you don't do some changes (updates of the core or testing newer php version).
As datakick advised:
1.4 is compatible with php 7.4
1.5 is compatible with php8+ but many modules will not be. It runs on 7.4 also.
So first install collectlogs module (or regularly read you error_log manually), roll to php7.4. If you have any issues with your module (errors, warnings, etc - fix them now!).
Roll to 1.4 if you're using an older version - fix errors and warnings on php7.4. Make db changes and fixes in Core module.
Roll to 1.5, remove tbupdater module (NOT Core updater module, they are different), update all native modules (if update is available), choose, install and configure email transport module (1.5 will not send emails out if this is not done, 3 minutes), install minification module (this was in the core, but was moved to a module for compatibility reasons, check if your code minification settings are proper in the old place where they were before, 1 minute). Make db changes and fixes in Core updater module. Look for new errors with your modules in Collectlogs module (core and native modules should work perfectly on php7.4).
Then update to php8.0 - again look for errors, if any - fix them.
And proceed to the latest php8 version you wish to use in the same manner.
DO NOT UPDATE directly from 7.3 to 8.2 - your shop will crash 99% (99% because of installed 3rd party modules).
At each step - make a USEFULL backup of your DB and file system.