This does seem to be related to
These settings are required in 2.4.3 but didn't exist in 2.4.2, and when testing still didn't exist after the patch until we actually changed the value and saved in admin.
In our case we had an error in the logs that the session size was too large at around 600000, so rather than set it to 0 to disable we set it to 800000 for now.
For our live site we had the looping 2FA but rather than disable 2FA and change session values in admin we just inserted the two records into
core_config_data with something along the lines of:
INSERT INTO `core_config_data` (`scope`, `scope_id`, `path`, `value`) VALUES
('default', 0, 'system/security/max_session_size_admin', '800000'),
('default', 0, 'system/security/max_session_size_storefront', '800000');