The thing about domestic cup competitions, particularly the LC is that you can win it by either being lucky or playing well in just a few games really. At least if you're also lucky with draws.
It is an achievement for sure. To me it can be an indication of progress, but it doesn't have to be. We could be more or less of a mess for the rest of the season, fluke the LC final and then finish the season poorly. Is there progress? I'd say no.
We could end the season strongly, get into the top four, win the LC, go far in the EL. Definitely progress.
A cup win like alone doesn't show progress, but it can be a good additional progress to progress elsewhere.
Wigan won the FA cup and got relegated. Is that progress? Now that's the more extreme example, but an example none the less.