This is one of the tensions I’m constantly fighting with in the worldbuilding (or lack thereov) around TFA. I could suggest that the Republic is falling apart under attacks from the First Order, but that begs the question of why they don’t use their defensive fleet and take action against these obvious aggressors. On the other hand, if I make the Jedi central to the identity of the Republic, then I run into the problem you state where the Jedi don’t feel like long-vanished myths.

The trouble is that without a clear source of something which causes the New Republic to become hopelessly overwhelmed by chaos, they will simply look inherently weak and incompetent. And if I try to describe exactly how the Republic is failing due to the complex factors of the Jedi being absent and the First Order’s agents infiltrating the Senate and causing gridlock and doing terror attacks with surgical precision to destabilize the Republic’s power and increase support for an Imperial style of government, well then I have six paragraphs with no signs of stopping.

I do see what you mean though. The film does portray the Jedi as essentially extinct and forgotten. I just need to thread the needle somehow, pinning the Republic’s problems on the lack of the Jedi while not specifically saying that the Republic is grieving at their recent loss.

JEDIT: Perhaps something like this:

It is a time of desolation.
Luke Skywalker, striving
to restore the light of the
Jedi Order, has vanished.

With his memory fading
into legend, the sinister
FIRST ORDER has risen
from a hidden stronghold
of the fallen Empire to
proclaim that anyone in
the New Republic with
faith in the ancient Jedi
shall be destroyed.

Appalled by this decree,
a few faithful Senators
have secretly lent their
support to the mission
of a brave RESISTANCE
to find the last Jedi and
restore peace and justice
to the darkening stars…