The tub looks horrible in the first picture, but before you judge me too harshly, know that I frequently bathe in baths with oil and coffee and weird things like that. So it’s not all grime.
Anyways, I cleaned my bathtub completely with just vinegar and baking soda! Cover the surfaces with vinegar (works best if it’s in a spray bottle, but you can also use my “gentle splash” technique). Sprinkle baking soda over that. Let sit for 30 minutes. Scrub with a sponge or towel. Yay!
Thought of this myself, but confirmed its efficiency with this article.