What can I use for an "acrylic-paint-looking" finish?

Just get some Krylon clear spray lacquer. Matte will be mostly flat, or try satin for a little sheen. It dries to touch in an hour, fully cured in around 24 hrs. Try a hardware store or even Michael's. Spray outside and try not to breathe the fumes.

You probably just got an acrylic paint with a "flat" finish rather than a glossy finish.

You can turn that into a gloss look just by coating it with a clear gloss finish (which will dry pretty quickly, especially in a warm, dry area with moving air like near a fan).

Or use a semi-gloss or satin finish if you want less glossiness; or just "sand" a too-glossy dried finish with 0000 steel wool then buff a bit, to take the glossiness down a bit.

There are various kinds of clear finish that will dry clear, from the toughest one, polyurethane (from a hardware store intended for use on bare wood originally...be sure and get an indoor, water-based, gloss version), to "gloss acrylic medium" or other gloss sealers/finishes available at craft and art supply stores.

Even a regular permanent white glue like Elmers GlueAll or other permanent white glues will leave a gloss finish when dry if they're first thinned down with water a fair amount (e.g., 3-4 parts water to 1 part glue in the case of Elmers GlueAll which is already pretty thin). Or "decoupage mediums" like ModPodge or Royal Coat are the same thing.

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