The full set of php settings available for you to configure in Trellis can be viewed in the defaults for the php role (and a few in the wordpress-setup role).
The group_vars/development/php.yml file is an example of overriding some defaults. Staging and production use the defaults and thus don’t have any overriding group_vars/<env>/php.yml files.
Ok you’re not using Bedrock. The only php differences I can think of that Trellis makes for development are in that group_vars/development/php.yml file. Could you try commenting out all those configs and rerunning the vagrant provision? Then the Trellis-controlled php configs should be the same for your dev and staging.
Any other differences between dev and staging would probably be in your own custom code, as far as I know. You might double-check your own settings for WP_DEBUG etc. Maybe also compare relevant php_info output from dev vs. staging.
Ok. If the above steps don’t help, just be sure you’ve researched these warnings enough to support the assumption that their display is a matter of settings in php (vs. something else).