Adjective for "impressive without seeming to try very hard"

Consider uncontrived.

Berlin Syndrome is an uncontrived thriller

ODO:

uncontrived ADJECTIVE

Not appearing artificial.

‘Some have praised the film for its uncontrived, natural feel.’

Since flashy is the opposite of what you want, you can start searching from unflashy, and then move onto its synonyms such as plain, unadorned, undecorated, unembellished, unornamented, unelaborate, basic, unsophisticated, no-frills; classic, understated, uncluttered, restrained, unshowy, and pick one that fits best after checking the definitions in a dictionary of your choice.

Just an example:

Understated -- Macmillan

(adj.) not trying to impress people or to attract their attention, and therefore attractive or effective
She dressed with understated elegance.

You use the word effortless in your question; but as far as I can tell it actually answers your question. The OED definition is:

Acting without effort; unstrained, easy.

This is often applied to a situation in which someone makes something "seem easy", without unnaturalness or artifice; it does not necessarily imply that no effort was exerted:

Dutch children’s theater company Het Laagland presents this formally innovative, effortlessly thrilling piece of physical theater about rediscovering the joys of play, shaking off the shackles of adulthood, and flying high with the king of make-believe.

(Brooklyn Academy of Music website)

In the end, the comic’s best trick is the illusion that comedy is effortless. That people imagine what he’s doing is easy is an occupational hazard. Cary Grant never won an Oscar, primarily, I suspect, because he made everything look so effortless. Why reward someone for having fun, for being charming?

(Richard Russo interview on failbetter.com)