Update and refactor `fm_yaml_mod` for new field_table format

[J-Lentz]

Description

• Update fm_yaml_mod and the field_manager unit test for the new field_table format
• Refactor and simplify fm_yaml_mod

How Has This Been Tested? Builds on the AMD box with Intel 2024.1 compiler; unit tests pass

Checklist:

• [x] My code follows the style guidelines of this project
• [x] I have performed a self-review of my own code
• [x] I have commented my code, particularly in hard-to-understand areas
• [x] I have made corresponding changes to the documentation
• [x] My changes generate no new warnings
• [x] Any dependent changes have been merged and published in downstream modules
• [x] New check tests, if applicable, are included
• [x] make distcheck passes