That reputation is more or less fabricated in order to shield the right from genuine critic. WP is not very left-leaning, I would consider them center. It's just that in the past 8 or so years the right has gotten much more radical, so it doesn't always seem that way.
My take is that WaPo has been exceptionally gentle with Trump, not at all holding him to the same standards they held Biden and Harris. From headline framing, to article vocabulary, to count of articles, fact checking, to associated photos, they've treated Trump quite hospitably.