Yes, «Тут есть овощи» is definitely more neutral.
I think «О́вощи тут есть» works best as an answer to «Тут нет овоще́й?» 'Aren't there any vegetables here?'.
It Latin it would be something like "olera hīc sunt" (not sure about the word order).
In Russian, the 3rd person singular form of the verb 'to be', «есть», has replaced all the other forms. «Есть» is indeed related to Latin 'est', but it's a singular form in Latin.
In some very rare bookish texts, you can find «суть» used for 3rd person plural. «Суть» is indeed related to Latin 'sunt'. But it would sound pretty weird if you used «суть» in a sentence about vegetables, it sounds well only in some technical texts.
Nice. At first I thought only the declensions were similar. Yes, of course "est" is singular (and the word order is fine. Latin is like Yoda. It likes its verbs by the end of the sentences), but what I meant is something that now I realised I can't really relate in English hehehe I am native of language derived from Latin and it is kind of difficult to explain my feelings about this sentence in English hehehe
Thanks a lot!