I will have a spare full day Sunday, coming from a work trip in Trieste. Staying near Mestre station.

should I go to Venice in the morning (have been there 20 years ago) or stay in Trieste and take train to Venice later that night?

If you've not toured Trieste, I would stay there for the day. There's a Roman theater to explore, along with the mosaics in Trieste Cathedral. You can also get to Miramare Castle by public.

All depends on your interests. There are tons of interesting places around Trieste, like Pirano, San Cassiano Caves, Lipizza or - between Trieste and Venice - Aquileia
https://www.discoveraquileia.com/en/

Prosecco is only 9 minutes by train from Trieste! Maybe a day (or part of one?) of tastings? 😁
🥂

Trieste I think

What time of year?

If Venice some time before the end of July, make sure you understand the requirements of the Access Fee.

https://cda.veneziaunica.it/en/access-fee

FWIW, the fastest trains from Trieste to Venice Mestre take 2.5 hours, so you're not talking about all that much time to explore Venice. The evening train journeys are longer.