docs: `integrations/providers/` update (#14315) #536

Job	Run time
lint / build (3.8)	14s
lint / build (3.11)	20s
pydantic-compatibility / Pydantic v1/v2 compatibility - Python 3.8	29s
pydantic-compatibility / Pydantic v1/v2 compatibility - Python 3.9	27s
pydantic-compatibility / Pydantic v1/v2 compatibility - Python 3.10	34s
pydantic-compatibility / Pydantic v1/v2 compatibility - Python 3.11	24s
test / Python 3.8	23s
test / Python 3.9	20s
test / Python 3.10	16s
test / Python 3.11	17s
	3m 44s

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