First, go back to your 2.263.4 setup, install OpenJdk 8 Temurin latest, (https://adoptium.net/marketplace?version=8), and you may as well also grab and install 11 for later.
Start Jenkins using jdk 8 as JAVA_HOME.
Consult the list of incompatible plugins from the dashboard (Tables to divs - Jenkins Jira) and disable (or remove) any incompatible as indicated in the 2.277.1 upgrade notes (Upgrading to Jenkins LTS 2.277.x ).
Before upgrading Core, upgrade all possible available plugins to latest compatible, restart. Validate.
NB: if you installed Jenkins a via a package manager, like rpm, DO NOT proceed to upgrade using this approach. Upgrade the package using the pacakge manager, as @halkeye answered well in a separate post.
If OK, then upgrade to 2.277.1, restart. Check the logs for any errors, especially relating to plugins on the restart. You may have to disable or remove those.
If you get the PKiX error again, this is well documented; google jenkins PKIX error
If running OK then immediately upgrade all the plugins again, restart and check again.
Repeat: read change log (LTS Changelog) and follow upgrade notes (Jenkins LTS Upgrade Guide) upgrade core to next LTS, restart, check logs, upgrade plugins, restart, validating as you go.
Once you get to 2.346.x successfully, stop, switch JAVA_HOME to OpenJdk 11, restart.
Now you can move to 2.361.x+, which requires Java 11. Then you are done.
Jenkins will not start w/anything other than 8 (up to 2.346), 11 or 17. Check the changelog to see what newer releases were OK"d for 11/17 if you want.