No, not manually. As you said, you are usually asked if the CRS does not match or is unknown, and then you can define it.
I think it is a known bug.
[SNAP-1335] Import of shapefile not working when reprojected - JIRA (atlassian.net)
good hint - when I delete the prj file of the vectors, I get the dialogue asking for a CRS
Strangely, the error message still shows up, although the coordinate extent of raster and vector is identical
295320.2181736761122011,4648695.9046654906123877 : 303130.7463378658285365,4662079.9147308627143502
Probably somewhere some wrong computation is performed.
Thanks for investigating and the hints. Will be helpful when looking into the code.