Sure, you can use the rules if you just assume they’re supposed to work in a way that makes sense and run them accordingly. But that’s not a defense of the way they’re written. The actual RAW very plainly implies that either the Hide action makes you impossible to find by sight alone, or the Invisibility spell does not. This doesn’t prevent a competent DM from recognizing that this probably wasn’t intended, and running stealth according to their intuition instead of according to RAW. But it’s a definite fault in RAW that such a ruling is necessary. It would have been easy to write the rule in a way that actually functioned the way they obviously intended it to.
As I already mentioned: stating that you are translucent in the spell description had helped.
Also a reminder that you need to try and stay unfound for you to stay invisible would not have been wasted words. Or a DM determines if someone notices you at the end of your turn of you are not concealed or behind cover.
I do reject your assessment that it is RAW that the hide action and the invisibility spell works similar. They have different conditions when the invisible condition ends. The spell does not say that you stop benefitting from the invisible condition* anymore when you are found.
So even if you deduce the location of someone who benefits from the invisibility spell with sight (leaving trails, carrying a light source, leaving a hole in an otherwise foggy area, detect magic?), they still benefit from the invisible condition. Actually since the spell does not even say you are translucent, we don't know how it works. Maybe the eyes actually perceive the enemy. But it makes people immediately forget the invisible person is there. (let me look up if it is an illusion or a transmutation spell... school of illusion).
If yoi deduce the location of someone benefitting from the invisible condition by hiding, being visibly in front of you ends the condition.
*also here is the rules thext for invisible:
While you have the Invisible condition, you experience the following effects.
Surprise. If you’re Invisible when you roll
Initiative, you have
Advantage on the roll.
Concealed. You aren’t affected by any effect that requires its target to be seen unless the effect’s creator can somehow see you. Any equipment you are wearing or carrying is also concealed.
Attacks Affected. Attack rolls against you have
Disadvantage, and your attack rolls have Advantage. If a creature can somehow see you, you don’t gain this benefit against that creature.
Nothing in it says RAW, that you can't actually be seen. You are just concealed. And if someone can somehow see you (in the hide case, by looking at you if you don't try not to be seen) the condition bears no benefit.