No nodes or edges after a successful admin import

I can successfully import data into an empty neo4j database using the following query:

.\bin\neo4j-admin.ps1 database import full --overwrite-destination db `
>>   --nodes="node_header.tsv.gz,node.tsv.gz" `
>>   --relationships="edge_header.tsv.gz,edge.tsv.gz" `
>>   --delimiter "\t" --array-delimiter ";" --verbose
...
neo4j 5.26.8
VM Name: Java HotSpot(TM) 64-Bit Server VM
VM Vendor: Oracle Corporation
VM Version: 23.0.1+11-39
JIT compiler: HotSpot 64-Bit Tiered Compilers
VM Arguments: [-XX:+UseParallelGC, -XX:-OmitStackTraceInFastThrow, -XX:+UnlockExperimentalVMOptions, -XX:+TrustFinalNonStaticFields, -XX:+DisableExplicitGC, -Djdk.nio.maxCachedBufferSize=1024, -Dio.netty.tryReflectionSetAccessible=true, -XX:+ExitOnOutOfMemoryError, -Djdk.tls.ephemeralDHKeySize=2048, -XX:FlightRecorderOptions=stackdepth=256, -XX:+UnlockDiagnosticVMOptions, -XX:+DebugNonSafepoints, --add-opens=java.base/java.nio=ALL-UNNAMED, --add-opens=java.base/java.io=ALL-UNNAMED, --add-opens=java.base/sun.nio.ch=ALL-UNNAMED, --enable-native-access=ALL-UNNAMED, -Dlog4j2.disable.jmx=true, -Dfile.encoding=UTF-8, -Xmx1048576k]
Configuration files used (ordered by priority):
...\conf\neo4j-admin.conf
...\conf\neo4j.conf
--------------------
Neo4j version: 5.26.8
Importing the contents of these files into ...\relate-data\dbmss\dbms-...\data\databases\db:
...

Importing nodes
...
Imported 8,537 nodes in 410ms
Prepare ID mapper
...
Range partitioning on node ID: NodeIdRange[numRanges:2, numNodesPerRange:4352, numRangesByNodeData:1, numRangesByRelationshipData:1]
Converting to intermediary format
...
Switching to bigger page cache for relationship import 32.79GiB
  using configuration:Configuration[numberOfWorkers=24, temporaryPath=...\relate-data\dbmss\dbms-...\data\databases\db\temp, numberOfTrackedDense=10000, applyBatchSize=64]
Importing relationships
...
Imported 9,683 relationships in 538ms
Flushing stores
Flush completed in 20ms
IMPORT DONE in 1s 483ms.

However, after I start the database Neo4j Desktop and open it in Neo4j Browser, when I query for the number of nodes and edges in the graph, it returns zero for both.

MATCH (n) RETURN count(n)
0

You need to create the database in system database. Select system database and run this Cypher. 'db' is the name of the database per your query.
CREATE DATABASE db
After this run: SHOW DATABASES . You should see your database name "db'" and scroll across to check its status. Once everything is okay then select 'db' from the dropdown list.

Your suggested solution involves creating a default database, start it, then in the neo4j Browser, create a new database named db then re-run the import.

Is this correct?

If so, I'm afraid I'm more interested in a solution that involves creating the database db from the admin tool at the time of bulk-import.

You mean like:

$ cypher-shell -u username -p password -d system "CREATE DATABASE myDatabaseName;"

or

$ neo4j-admin database create myDatabaseName

(you can't create and import on the same statement ... you need to create, probably pause for a few seconds or checking the script's output, then import)