In a nutshell, "to soak" = to immerse in water (or under water) "to soak up" = to absorb, to bask in (sunlight or fame)

Soak in is indefinite in extent or duration. Soak up implies/connotes an unmentioned completeness or totality (deliberately not said, usually due to the compactness of casual speech or for imprecise reference).

I think the most essential thing to learn here is not the difference between the verb "soak" and the phrasal verb "soak up" containing a particle (preposition or adverb in phrasal verb mode). Instead it is the particle "up" after an action, usually a movement, verb. Get up, Go up/down, move up, drink up/down, and throw up come to mind. I have not found any discussion about up/down as particles in phrasal verbs in my most essential sources on English usage from Oxford as Fowler (Modern English Usage) and Gardner (American English Usage). That is regretful. Yet I have always taught that they rather imprecisely though deliberately imply the added general meaning of "completely," "wholly," or "totally" in addition to the verb they are used after. Still this seems true only about 80% of the time. But that much works superbly for students in rule-oriented grammar, EFL/ESL/L2 purposes. Thus soak down would imply completely taking up or in a liquid, idea, concept, belief, etc.

To soak something - To make something very wet. To soak up something - To use another thing to receive water/liquid to make it dry. OR We can also use it metaphorically, such as 'soak up sun', 'soak up knowledge' - means to receive sun/knowledge (lots of it, and very easily).

To "soak up" is to absorb something. Like a sponge soaks up water. When i hear "soak up the sun" I think of absorbing the warmth of the sun and the sun's rays. It feels good and is very relaxing. When a downpour "soaks the spectators", it's negative. I think of being completely wet (like getting out of a swimming pool with all of my clothes on). It is worse then just being wet. It is being gross and miserable, and probably cold too.