Yes, KMCP provides some prebuilt databases for genome searching, no Genbank but you can use GTDB. Here's the tutorial.
Sourmash provides databases for GTDB too, and old Genbank databases (2018) are also available.
Both tools work great, the biggest challenge is downloading the whole Genbank database. Building the database using a sketching algorithm is also fast.
If you know the taxid you can find the closest whole genome using
gaas_ncbi_get_genome_tree.plfrom GAASI don't know taxid. All I have is contig sequences.
There is no such tool that align a draft genome against all genomes in Genbank. First you must identify to which taxonomic lineage (taxid) your draft genomes belong. To figure out the taxid get the 16S from the annotated genome or use the Type Strain Genome Server to find the closest type-strain