Surely seems to be a wetland by your definition of its properties; do a lot or research before thinking not.

try: https://www.epa.gov/wetlands/what-wetland

the pool might be a listed wetland and you don't know it; your photos certainly gives the looks of a large vernal pool; many years ago farms dung shallow pools for water for their animal stock and gardens or fruit tree groves which developed into wetlands over time.

My farm has two hand dung vernal wetland pools -- they are protected by federal law

although it is most difficult to get caught...you are fortunate to have the size and variety of animal life...maybe your acres has a space/area to build a pond properly shaped and dug for fish and swimming -- man and dog

as others have said be careful; get professional experienced help to 'refurbish' what nature manages [perhaps man made, perhaps nature made, either way you have one beautiful pool]