Magento 2 report.WARNING: Session size of xxxxxx exceeded allowed session max size of 256000.
After updating to Magento 2.4.3, there is an error that is not directly related to PHP or nginx that can cause some headaches in the admin, usually in the form of an error message and pop-up that has to be acknowledged on every page load (see above).
In the var/log/system.log, it will show up as:
[2021-08-16 19:22:52] report.WARNING: Session size of 375349 exceeded allowed session max size of 256000.  
A quick fix for this is to set the limit to "0" at the cli. It can be accomplished with the following command:
bin/magento config:set system/security/max_session_size_admin 0
Run the command above then flush cache:
then you're all set!