〜そうです

seems to be

behaves as なadjective

MNN43-1

We use this form to describe that it looks like something is about to happen.

今にも雨が降りそうですね。
これから寒くなりそうですね。

いadjective
adj+そうです
negative
~ない ⇒ ~なそう
おいしくなさそうです。

いいです ⇒ よさそうです
よくないです ⇒ よくなさそうです

なadjective
adj+そうです
negative
しずかじゃない ⇒ しずかじゃなそうです。

verbs
Vますstem+そうです。

Though あります is a verb, phrases like 時間がある, お金がある are more like adjectives in that they express states or property. So you could say things like “he looks like he has time” or “he looks like he is rich” will look like:

あの 人は お金が たくさん ありそうです。
あの 人は お金が なさそうです。

あの 人は 時間が ありそうです。(ひまそうです)
あの 人は 時間が なさそうです。(いそがしそうです

likewise
Stative verbs like: 知っています、住んでいます, as in “he looks like he knows a lot about Japanese” or “he looks like he lives in an affluent area” etc.
Even normal verbs like 食べます、飲みます, as in “he looks like he eats a lot” or “he looks like he drinks Guinness”

note
Adjectives such as うれしい (happy), かなしい (sad), etc, are not used as they are to describe other people’s emotions.

ミラーさんは うれしいです。✕
ミラーさんは うれしそうです。✔


from Stack exchange →

そうです indicates a similarity based on direct (probably visual) evidence i.e., David appears/behaves like a good chef based on what you see.
In this usage, そう is attached to the i-form of verbs and stem of adjectives.

(だ)そうです is a report on what you've heard before.
In this usage, そう is attached to the dictionary form of verbs, directly to i-adjectives, and with a だ behind na-adjectives.

ようです like the first そう, indicates an appearance you are directly observing, but more certain - a higher likelihood - than そうです. That is, David looks like he is good at cooking based on how you're seeing him cook. よう is attached to nouns and na-adjectives with a の in between.

らしいです indicates its something inferred from indirect evidence. In other words, David seems to be good at cooking (based on what you're heard).

Note that ようです can also be a somewhat non-committal observation. And らしいです (or more accurately, just らしい) can be used to describe an attribute, similar to using -like in English. e.g, 名探偵らしい → detective-like, like a good detective, in a good-detectively sort of way.